Hide Shipping Methods based on Shipping ZIP Code

I have a customer that is sending gift baskets to volunteers within their school district. The volunteers can pick their gift basket online and if they ship to a ZIP code within the school district, it should enable the shipping method (and show that shipping is free). If their ZIP code is outside of the school district, then they cannot place the order. Any idea of how to do this? I don’t want to install an extension for something like this if I don’t have to.