In May of this year we received a similair letter from our City Administrator. It cited the code and said that poultry was considered livestock. The difference beeing that the only way you could keep livestock in the city limits was by the written consent of the City Council. We jumped through the hoops and got on the agenda for the next meeting. At the end of a long half hour where no member wanted to make a motion, almost dead silence, it was decided by a vote of 4 to 1 to let us keep the chickens as long as we kept them penned. Our coop is in the garage and we fenced in the area under the deck for the birds to run in. We still let them out but only when we are home for a bit in the evenings to free range so as to gather no complaints. We have far more people who find it interesting and support us. we also have great neighbors. The birds also go to school on occassion to entertain the Headstart children.
Perhaps, just perhaps you could ask for some time to bring this to the councils attention. To find examples of the growing popularity of urban chicken raising and sway them to change the code. Thats how it is done. Do not delay. It does not take a lawyer to add an item to the councils agenda. I responded as directed with a very up beat positive letter addressed to the city council and to the administrator, that the Mayor really liked. It may also buy you some time.
At the end of the day, proper chicken raising, respecting others and being willing to compromise is how these things are accomplished.
Best of luck to you and if I can be of help, don't hesitate to ask. My argument was that our chickens are pets too. They are show birds and they are. We do not process ours for food and we are not an agricultural business.