Zimbabwe does not have a post code/zip code that I know of, however, I always input 9990 into the mentioned field and the website accepts it.
When you are shipping to Zimbabwe, be sure to stay away from "courier shipping" that is your DHL and FedEx's. They will rip you off.
If buying from China, opt for free shipping, it will take 30 - 60 days, but you collect it from the Post Office and just pay $2 for handling (if there is no duty - no duty usually applies when the goods are worth less than $10 or is a very small package).
If you pay duty, then the post office will require $10 for your shipment. They also charge you based on weight, so be sure to check the price at your nearest post office before buying.