On the Sega Genesis there are codes that unlock a level select, debug mode, and one that gives you all 7 chaos emeralds from the start. They work in this version too. These are the codes.
On the title screen, go to options. Select the sound test and play these sounds in order to get the level select. 19, 65, 9, 17. When you play 17, you should hear a ring sound. Go back to the title screen and hold the button you set for 'A' and press the button you set for 'start'. This will take you to the stage select. The stage select lets you choose what level and act to start from, and has its own sound test.
To unlock debug mode, go to the stage select and play 1,9,9,2,1,1,2,4 on the sound test. You should hear a ring. To play the game in debug, hold the button you set for 'A' and press start.
To get all of the chaos emeralds, play 4,1,2,6 on the level select's sound test. You should hear a the sound you get when you get a chaos emerald. Now get 50 rings or more and jump to turn into super sonic.