Shot in ODO
1 (of coloured cloth) woven with a warp and weft of different colours, giving a contrasting effect when looked at from different angles:
a dress of shot silk
- interspersed with a different colour: dark hair shot with silver
- (shot through with) suffused with (a particular feature or quality): the mist was shot through with orange spokes of light
It's not a repeated pattern; it's a highlight of some sort, either the odd thread, or the entire warp or weft.
In the quote, it could be either, but since a different warp and weft would give rise to "a truly beautiful shade," it's probably that: woven throughout with two different colours.
I couldn't find an example of grey and red, but here's blue and red from the blog Snoring Scholar: