Not sure if I can help or not, but I do have one question, are you sure you got the DOS version of HOMM?? They did release a DOS and a Win95 version. They were available separately and from memory I think they did have a CD which had both versions on it. I just ask cause my HOMM is Win95 only and is no way it would work under DOSBox cause it needs DirectX.
HOMM was one of those titles released when Win95 first came out so it was originally made for DOS but not long after converted to a Win95 DirectX version. So depends which one you bought. If your not sure best way to find out is look on the CD and see if there is any sign of DirectX.
If you do have a Win95 version it does work under Windows XP, just use compatibility mode on the CD Setup.exe file, then run game as normal (not using compatibility mode), the map editor will need compatibility mode to run.
Good Luck.