There is no need to embed the post code on every page. Just make sure to embed it into your most visited page (you can use the Cpanel of your hosting to see what page is visited more) and perform SEO optimization for that page then you will be found easily. However, you might need to assign a different word to the postcode because, for example, if someone searches for that post code and you don't have something else attached to it, you will be hard to find in these conditions.