two weeks ban for first offense means a Rioter personally gave you the ban, by whatever means they have.
It also means that you won't get a reform card.
And it also means that if you get banned for the tribunal after your ban, it will be a permanent one, straight.
What you CAN do however, is send a very nicely and politely written email to support, and ask them two things
"Can I please know why I have been banned for two weeks for a first offense?"
"Could you please tell me how I can improve in a manner to prevent any more future punishments?"
after those, add all info about your account (Email, Login, estimated date of creation, date of your ban, etc. Just don't send passwords.).
If you follow these simply instructions, then you will have good answers.
Here is the link, I hope to hear again from you when they replied.