MapEdit++ seems to run OK under Wine.
But if you get an error when loading images:
wine: Call from 0x76560b80 to unimplemented function
wine: Unimplemented function gdiplus.dll.GdipGetImageDecodersSize
called at address 0x76560b80 (thread 0014), starting debugger...
Unhandled exception: unimplemented function
gdiplus.dll.GdipGetImageDecodersSize called in 32-bit code
it means that GdiPlus.dll from Wine is broken. Please copy GdiPlus.dll from Windows XP (please update your Windows with WindowsUpdate before copying, don't use old buggy version) and replace the Wine version of GdiPlus.dll. It should work now without problems.