Tim Campion already pointed out FAQ post the question: What can I do to lift or reduce a suspension? I will add also link to another answer on Meta Stack Exchange: Where I can complain about an unfair account suspension?
Apart from replying to the moderator message, you can also use the contact form to contact Stack Exchange Team. On MathOverflow you have also an option to contact the MO moderators using email. (This is specific for MO, other Stack Exchange site do not have such option.) In an older discussion it was mentioned by a MO moderator that this is a possibility how to object to a suspension.
If you use the first option, you're communicated with the Stack Exchange employees. The second option means contacting directly the MathOverflow moderators.