I have been banned because my mate was at my house and he typed something rude and I have been ...

You can try submitting a case review at
http://enforcement.xbox.com However, you are responsible for your account at all times.

here is a quote from the xbox enforcement site:

''

My roommate was playing when I got suspended. Can it be lifted?
Xbox Live is a social platform, and we love hearing about players sharing their experience with friends and family. Xbox Live is at its best when everyone joins in the fun!

However, as the owner of the account you are ultimately responsible for how the account is used, both good and bad. When we issue a suspension, it’s not necessarily because you committed a violation, but because the account was used to commit a violation.
Even if you weren’t home or holding the controller when the activity occurred, if a particular Gamertag was used to harass other players or cheated in a game we have to hold it accountable.
''

source: enforcement.xbox.com

so basicaly you will be held responsable for anything that appen ON YOUR ACCOUNT (since its your account)

and also microsoft cannot determinate if you or someone else is using your account (especially if you share your loggin info or grant access to yous xbox to anyone)

therefore it is your responsability to make sure your account is properly used.

it was your account

Thus your responsibility

Hiya Ace,

Thank you for your reply.

If you've removed and replaced your security information within the last 30 days, you'll have to wait until the 30-day period is over before you can do it again. This waiting period helps protect your account if an
attacker gets your password.

After you've updated all of your security information:

The update takes 30 days, and during that time you can sign in on your consoles, but there will be certain things you can’t do with your account.

Here's what to expect after you've updated your security information:

The security information you chose to remove will be deleted in 30 days. During that time, we'll send notifications to the phone number or email address that's being removed,
in case an attacker is attempting to remove your information.

We can't expedite this process:

You'll be able to continue using your console during the 30-day waiting period, but you won't be able to make changes to your password or use your account to make purchases online.

You'll be unable to make security changes to your account or manage parental controls online.

(If you already have your account on the console there should not be an issue, but if you are trying to add the account to the console then you need to validate the account. Or if there is a

Two step Verification on your account, there will be addition information that needs to be verified)

Hope this helps.

Hey Aced thanks for keeping in touch!!

If the issue is persisting then at this point we suggest as previously stated to

Request a Callback from one of our Xbox Support Specialists so we can further investigate the issue on the account and hopefully get this issue resolved!