If Zipcode is unique per customer at that time, Your customer can be login using zip code. Because I think its not proper way to log in using zipcode because one Zipcode has many customers and how to define for those customer using Zipcode. It is not a valid scenario.
If Only one zipcode per customer at that time you need to customize core file,
vendor/magento/module-customer/Controller/Account/LoginPost.php
In above file You have to override first and then customize based on zip code. You must assigned zip code at a time of registration so customer contains zip code and its unique one.
