From experience most apologies here, no matter how sincere, don't seem to be effective and you'll unfortunately probably just have to serve the time.
Yeah, you can whine, whinge, rage and apologize but from what I've seen in the past it won't get you anywhere. If I were you OP I would simply take the ban as a warning and a lesson to avoid mindless posting in the future and just wait it out. Two weeks isn't particularly long - just avoid the urge to open another account, you will be banned for ban evasion and your main account will get a further ban. Just take it as a cooling off period.