This is exactly what one expects from a pinhole lens.

Normal lenses

A normal lens has a big opening and bends all the light rays coming from a point-like object to cross in a point behind the lens. By moving the lens fore and back, one can determine the position of the point behind the lens, and when it's exactly on the sensor, it might hit a single pixel only. (In theory.) So, a point-like object would be projected to a single pixel, which is the maximum sharpness you can get.

At the same time, light rays from other point-like objects in other distances are bent so that they cross at a point in front of or behind the sensor. This gives circles of light on the sensor, hitting many pixels. So, those objects are unsharp.

This is illustrated in the following image I made using a simulation. There is a 50mm lens and three point-like light sources placed 800, 1000 and 1200 in front of the lens. A screen (=sensor) is placed 52.63mm behind the screen, where the light rays of the middle, red light source cross.

(Click to enlarge)

This zoomed-in image shows how the blue and green rays cross in front of / behind the screen and form larger spots on the screen. (The black dot is the focal point of the lens)

Pinhole lenses

A pinhole lens only has that pin hole, but no optical lens. That means that the rays entering through the pinhole will not be bent to cross at a point. They travel in the same direction as before, and form a spot of about the size and shape of the pinhole on the sensor. This means, if your pinhole has 0.22mm diameter, you get a 0.22mm circle on your sensor. For example, my camera has a 22mm wide sensor and the photos are 5200 pixels wide. The 0.22mm circle-shaped spots from the pinhole lens would result in circles of 52 pixels diameter on my photos. Quite blurry!

Now, while the optical lens inside a normal lens can move forth and back to focus objects in different distances, the rays from objects in all distances entering a pinhole are about parallel. (Except for objects very close to the camera) So, all objects show about the same unsharpness.

Here are images with the optical lens replaced by a pinhole. Since a 0.22mm pinhole would not be practical here, I exaggerate it by using a 5mm pinhole, but the principle is clear:

Due to the heavy overlap, the three light sources could not be distinguished.

Setting the focal length

I wrote that focal length is a pure informational value in your case, but as @junkyardsparkle and @mattdm pointed out, that's not true.

Today, cameras have image stabilization techniques to reduce blurriness due to small shivering movements when the camera is hold in the hands. Some cameras like DSLRs from Canon move the lenses sidewards, while others like yours can move the sensor instead. The focal length is needed to calculate how much the sensor has to move to cancel out a detected shiver.

Diffraction?

An other user wrote in his answer that diffraction is the cause of the blurriness of the image. Well, it's not that easy here.

In general, diffraction exists, and I'd like to link to Wikipedia about Airy disks for further details.

The important formula is

• λ is the wavelength, for the visible light 400-670nm
• d is the diameter of the pinhole
• θ is the angle between the center of the airy disk and the first ring of absolute darkness around it (which can be seen as boundary of the disk), as seen from the center of the pinhole.

Now, with your numbers, one gets θ=0.001818rad for violet 400nm light, and θ=0.00302rad for red light. This multiplied with 48mm, the distance between pinhole and screen, gives the radius(!) of the airy disk, so one has to multiply by 2 to get the diameter. Then, the diameter is 0.17 to 0.29mm.

OK, so indeed, the spot on the screen is larger for red light if diffraction is considered. But wait, it's smaller for blue light?

Well, those formula imply that the diameter of the spot is zero directly behind the pinhole, which obviously is not the case. Those formula are correct far, far away from the pinhole, and our screen is not yet so far away.

This image demonstrates this. About 100mm behind the pinhole, the spots are really much larger due to diffraction, but at about 50mm, well, a little.

In case of a normal lens, diffraction plays a bigger role at high F-stops. A perfect lens would focus the light beam to a single point, but the diffraction makes it a spot with some diameter, or even some pattern.

Notes

One could write a book about everything that affects the image quality. For example, the real lenses here are considered ideal. For the pinhole lens, the precision of the hole, but also the thickness of the material plays a big role.