If it is saying due to spam and plagiarism then how come it's unknown reason :-)
Anyway, if you are really sure about that you have not done any plagiarism or never done any spam then we my expect an explanation from Mod or whoever banned the account.
Sorry to hear the situation.
I guess you mean apply for unban?
Did you plagiarise?
If you did plagiarised and with such negative trust (bad net effects), I don't think you can get reduced sentence from your permanent ban.
I do not think this should have any connection with unbanning or reduce sentence.