This has worked once and failed once for me in the past.
Simply say that another family member that has access to your computer and your password was able to dothe offence and that, as your previous history will show (assuming you havn't got any other offences), you have never done anything of the sort before. Say that you have learnt your lesson about trusting others and will not do so in the future.
This ticks all the right boxes:
1) Explains why your ip made the offences
2) Seems out of place on an account with no offences
3) Shows measures of prevention for the future
I have however noticed that depending on the type of offence they either ignore it or semi ignore it. If you are one of the lucky ones that has their appeal read by a person you have a chance. A slim chance but a chance.
Good luck though!