i am not 100% on this but i had a key for another car coded a while ago and the cheapest way to do it would be go to a scrap
yard see if you can find a key then go to the dealers and ask for all your codes it cost about £20 but you will need to take your log book and drivers licence they keep all the codes on file so they can charge you a fortune when you need a new key i think it takes them a day to get them they need to order them, then just find a lock smith or an auto electrician to code it in..
like i say im not 100% because it wasnt an audi i had coded so i dont know if its the same..