Homebrew Channel and Mario Kart Wii are very different matters. There's plenty of videos on YouTube about it, but I'll give you a quick run-through.
NOTE: If your Wii System menu is version 4.4 or higher, you cannot get Homebrew Channel: End of story.
If your Wii is version 4.3, you can use Super Smash Bros Brawl Smash Stack in order to obtain Homebrew Channel (this is how I did it). This method works for USA Europe and Japanese Wiis, not Korean.
There are other ways to get the HBC with lower versions, which I don't know so you could search up on youtube.
Okay, Mario Kart Hacking:
When you have Hombrew Channel and Browser set up, you need to download Ocarina or Gecko (I use Ocarina) onto your HBC.
Download code manager onto your PC and must have SD Card NOT SDHC card. Transfer codes from your computer to your wii.
Watch tutorials on how to do it, they'll be better than me. :)
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