Span means something goes from point A to point B, so I think saying "span" and "all around" is a bit confusing. As P.E. Dant points out, "span" doesn't typically take a preposition (except maybe across, which would probably be redundant most of the time).
You could try:
Doors span the entire room.
Or something like:
Doors span the length of every wall.
Still, I think this is opening you up to a potential ambiguity: Do we have a bunch of doors in a row, or are the doors just super wide? Also, even if we don't have super wide doors, do they doors really span the entire wall/room, or are there just more doors than normal? If you say the doors "span the length of the wall," you're really saying that it's just door after door after door with no spaces in between, and I don't know what kind of crazy room that'd be true for.
If you really want to say "there were doors all around the room," I'd just say that. Or "the room had a lot of doors" or "there were multiple doors on every wall of the room" or whatever more specific thing you can think of that is accurate for the circumstance.