I do not know what you mean Zimbabwe is not listed on the list of countries. Go to paypal.co.zw and you will be redirected to Paypal's own Zimbabwe page with the options preselected. Zimbabwe does not use Zip codes so any four digit code will work just fine, if you are asked for it. I use 0263 myself but it does not mean anything.
What card are you using? The Ecocash debit card is a mess when it comes to Paypal.