What exactly does 媽个八子 mean? Are those the correct characters? I understand it to be profanity but how bad is it? Worse than 你妈的 ? Any insight would be appreciated, just find this to be a funny expression that I haven't heard of before.
Well, I agree that @NS.X said. 

First, it should be "妈了个巴子", not "妈个巴子". 

Second, it is much worse than "他妈的". 

Actually, if you are angry with something, you can say "他妈的", to express your dissatisfied emotion. But please do not use it to a person. However, please do not use "妈了个巴子" even if for a thing, since it is too coarse. 

Anyway, it is not good to say these kind of word in China. Others may look down on you.