The only way you could say this is, "I don't have such an amazing heritage" or "It's an amazing heritage, but one that I don't have." The problem with using "never" is that you are either born with a heritage or not--it's not something you do like, e.g., visiting Brazil or surfing. Saying you've never had a different heritage is like saying, "I've never been Japanese."

How about, "...such an amazing heritage which I haven't had"? If you want to use "never"("not ever"), then change "had" for something better. "...such an amazing heritage which I had never experienced before." "...such an amazing heritage which I had never known before." (I added "before" because now you have some knowledge or experience of this heritage.)

what great grammar peachy has! *bow*