Well, I googled Basket Weave Quilts, like ckcowl suggested, and now I realize the Rail Fence is not at all what you were looking for. I looked at the quilts on Pinterest, and I saw one that looked like what you described...lots of squares with really interesting thick thread borders....and I liked that quilt!
I look forward to seeing a picture of yours, but I suspect it is still a very good looking quilt! Just not what you had in mind when you started....
Dina