This might not be a faux basket weave so much as a simple one. My sister-in-law requested a silver belt. I wanted to make it interesting but I was limited to yarns that included metallic silver strands. So I decided to try doubling some of the warps. I'm really happy with the results. It's a subtle addition to a simple belt. It gives the piece a more sophisticated feel.
The texture was difficult to photograph. You'll mostly have to take my word for it. I played with Photoshop a little and got a posterized photo which might help you see the detail better. Or it might be worse. dunno. Guess you'll just have to weave your own?
The middle section is the basket weave. The darker grey borders are a plain weave. For the middle, I doubled every third warp.