At the "Push Start Button" screen, press Triangle, Down, Up, Triangle. If you entered the code correctly, an icon will appear in the top right corner of the screen. Select puzzle mode or arcade mode to access additional levels.
Bonus characters
At the "Push Start Button" screen, press Triangle, Up, Down, Triangle. If you entered the code correctly, an icon will appear in the top right corner of the screen. Weepy and Smiley will be unlocked in all modes except for story mode.