Does anybody know what coordinate system this could be?
Impossible to say. Its corners are pretty much (0,0) and (4000,-2827), and I bet if the image is 4000 pixels by 2827 pixels then its not got any coordinate system attached to it at all.
If you know where its meant to be on the earth then you could use something like the "projfinder" website to figure this out. But I'm guessing its not got a reference system and its just indexing pixels from the top left.