There are no cheat codes for the Burnout Paradise Demo on Xbox 360. Demos are stripped-down builds; cheat support is typically disabled or non-existent.
Why cheats don't work/aren't advised:
Better Approach: Enjoy the demo as intended—learn the map, practice takedowns, and test driving physics. If you like it, buy the full Burnout Paradise Remastered (PS4, Xbox One, Switch, PC) which has full content, better graphics, and all DLC included.