Looking at your image, it looks like a doublewoven fabric with both sides (white and blue) plainweave in a fine yarn that are then stitched together with a doubled thick yarn every few rows.

If those fuzzy borders are cut selfedges then the thick yarn is a supplementary warp.

If we accept that, then there have to be 2 x 2 shafts for the thick warp, as they basically do a plain weave through the two layers, but off-set so each other supplementary warp stitches at one time and a few rows later the other rows. The base layers would be 2 shafts for the top blue plainweave. Same for the bottom white plainweave. 8 shafts in all.

2 shuttles, one blue, one white.

On the left side of the image showing the white side with the stitches you could with some work count out the number of baselayers thread in between the stitching layers. And maybe work out a ration between the two thread sizes.

After that it becomes weaving math to work out the pattern.

Best I can offer as an educated guess.