I was able to use a Action Replay code for X-Men Next Dimension, after following the steps described in
http://forums.ngemu.com/dolphin-discussion/108204-how-add-cheats-dolphin.html
Strange things keep happening though, because I tried two relevant cheats I wanted to use, and although the Unlock all characters cheat worked, the Unlock all costumes apparantly doesn't, even though I went about decrypting them both the exact same way, sigh...
The examples in the patches folder both have a "company code" of 01 which stands for Nintendo of course, for X-Men Next Dimension, it's "GXME52".
Still can't start a match anymore like I used to (dunno why..?) but the cheat system works kinda... Now to get the game back to working again like it used to...