Section 468 of Indian Penal Code is a non compoundable offence. Hence, compromise between the parties does not empower the High Court to quash this criminal proceeding.
The High Court can quash the FIR if no offence is made out against the accused. If the allegation in the FIR is bald and frivolous then the High Court can quash the FIR.
No such things happened in your case, therefore, the High Court cannot quash this proceeding. If the trial court finds that prosecution has failed to prove the guilt of the accused, then it can acquit you. There is no other method to conclude this criminal proceeding.