That is actually not true.
It may be difficult, because it requires your code to be part of IOS, you'd have to create a custom IOS that does exactly this, which isn't easy. Also, IOS has no access to video/audio output, but that may not be a problem. May I ask what your "little code" should do?
At one point, WiiConnect24 might be understood enough to allow homebrew using WC24 to execute small pieces of code. However, the WC24 method will not execute games while you are running games that don't do WC24 communication (many old games and third-party games don't). Using the IOS method, you could run code in the background, but not constantly, it would start over at each IOS reload. Furthermore, you'd have to modify every IOS used on your Wii if you want a constantly running background service.
Anyway, it's difficult to do, but not impossible. I'm confident that at least WC24 will be an option eventually.