tl;dr: Talk to your employer and ask for an Auflösungsvertrag.
Regarding the maximum consequences, there are
- the one month gross salary penalty your contract mentions
- any damages your employer decides to claim from you (and is able to defend in court eventually & recover from you). Worst case scenario, you are a crucial employee on an important project and because of your unforeseen departure your employer is unable to deliver to the client. They could claim a large part of their lost revenue from you as well as compensation for reputation loss (and related lost future revenue).
- on top of that, should there be litigation, expect to be faced with major process fees (lawyers, courts, ...).
While it is not a given that your employer will ask for all of that, the only sensible advice I can give to you is to talk first to your boss and then HR department yesterday. Explain yourself and ask for an Auflösungsvertrag/Aufhebungsvertrag, i.e. a contract that terminates your employment contract. Your employer has no obligation to accept this, but you can increase your chances by making concessions that are beneficial to them, e.g. staying for two more months instead of only one, agreeing not to take any leave in the remaining time, finishing important projects you are currently working on ...