To access the cheat menu, go to the setup screen and hold L + R + Z. While still holding them press all four of the C buttons. If done correctly under audio should appear cheats.
To access the codes in the cheat menu simply put the cursor on the code you want to access then enter one of the codes below:
Massive Mass
Hold L and R and press C-Up, C-Down, C-Left, C-Right
Killer Rats: Hold L and R and press Z, Z, Z, Z
New York Cabs: Press R, L, Z, C-Up, C-Down, C-Up
Resurrect In Place: Hold Z and C-Left and press C-Right, then hold Z and C-Right and press C-Left.
Frame Scale: Hold Z and C-Down and press C-Up, then hold Z and C-Up and press C-Down.
Tire Scaling: Hold Z and C-Left and press C-Right, then hold Z and C-Right and press C-Left.
Auto-Abort: Quickly press C-Up four times.
Game Timer: Hold Z + C-Down, press C-Up, then hold Z + C-Up and press C-Down.
Invisible Track: Hold L and R, and press C-Down, C-Up 5 times.
Brakes: Hold C-Up and C-Right, and press Z 3 times.
Super Tires: Hold L and R, and press C-Up, C-Right, C-Down, C-Left 2 times.
Suicide Mode: Hold Z, and press C-Down, C-Left, C-Up, C-Right 2 times.
Do the Dew!: Press L + R + C-Down, then L + R + C-Left, then L + R + C-Up, then L + R + C-Right twice, then press Z.
Levitation: Hold L, R, and Z, and hit C-Up 4 times.
Fog Color: Hold Z, and press C-Left, C-Up, C-Right, and C-Down 3 times.
Stunt Mode: Hold all four C buttons and press R, A, Z, L.