You can estimate it with similar triangles. For a 35mm-equivalent focal length of 38mm, the full-frame sensor height is 24mm, so:

38 : 24 = 14,000m : height

height = 14,000 × 24 / 38 ≈ 8,842m

So if the subject fills nearly the full image height, its height is about 8.8km.

A few caveats:

• This is only an approximation; “almost the full height” introduces some error.
• If the subject fills only part of the frame, scale the 24mm by the fraction of image height it occupies.
• The estimate is best if the camera was held level. Tilting the camera can affect the apparent height.
• The 35mm-equivalent focal length is convenient here because it already maps to the standard 36×24mm frame.

For something like a volcano’s smoke plume, this gives a reasonable ballpark figure, likely within your requested tolerance if the distance estimate is good.