This server does not support the use of accounts that were not bought from the official Mojang website.
If you bought or got this account from someone else, there is probably nothing that can be done about your ban. Account trading is forbidden by the EULA and therefore the server doesn't allow these accounts online either.
The only way for you to (rightfully) play on the server is to buy an own account from Mojang.
If you're banned via BAC, try joining with Vanilla or any other client.
But I don't think you should be banned from the server if you were just banned by BAC on another server, kinda weird.
And generally speaking, just create a ban appel at https://guardian.gommehd.net/, your problem will most certainly be solved there.