So although pretty much every cheat code from 1.3 is intact in the 38A version, aside from some minor changes to some due to removal of sprite masks or the like. However, there appear to be some other cheat codes that are in this version as well. If you find anymore, please make a reply with the cheat code you typed.
Current cheats discovered:
needafrogsuit - puts a Frog Suit in the player's reserve
needastarman - puts a Starman in the player's reserve
needaminimushroom - puts a Mini Mushroom in the player's reserve
needapenguinsuit - puts a Penguin Suit in the player's reserve
needapropellermushroom - puts a Propeller Mushroom in the player's reserve
Other possible power-up codes like needamegamushroom don't do anything, probably due to causing a possible runtime error if Peach or Link are the playable. As for needablueshell, it works, but obviously it's not the Blue Shell powerup. If you find a code for it, please reply.
Based on this, I'm sure there would at least be a few other cheat codes aside from these, so if you find anything, don't hesitate to let me know.