Without knowing what language got you banned, you apologize for it and claim to never use that language again. How are you going to accomplish this?
Let me just post what information we have regarding your ban, warning and second ban.
At around may 10th 2014 ethe334 banned you for language.. This ban was later turned into a warning: see
here.
Later on September 19th 2014 you received a local ban for swearing: see
here. As you already noticed you weren't banned while you were logged in to the server. We keep an eye on what's happening on the server even when we're not on.
So you received a pretty severe warning (accidental ban, then warning). And then later you used your keyboard to write down language that you know would get you banned on our server.
With this information, please feel free to add to your appeal.
I'll leave the rest up to Jiro.