1. After exiting your cell, Haru and Ann will talk to you
2. You go to the welcome party that's at Gasoline
3. You rest back in your cell
4. You go back out to meet up with Matthias
5. You go look for a character named Enzo who is at 2-E165 and give him items to get certain things like passcode and info. He's on the third floor.
6. Go to the Cell Garden at 2-G100
7. Go to the weapons shop and talk to Julian
8. Go retrieve an item for Julian. Located in 1-E020, after retrieving red colored item, return to Julian and give it to him.
9. Head to the Cell Garden again at 2-G100
10. Go to the one where you need to sneak around guard accessories. afterwards at the end, you'll get caught and 200 or 400 years will be added depending. Getting caught by the guard accessories during the sneaking around adds a few years to you and they throw you out.
11. After that you should head to Gasoline and talk to Julian, where he'll give you 2-2 mission.
This should be the correct way to do it. hopefully this helps.