It's another form of "to beat all", akin to "that beats everything".
From the American Heritage Dictionary in Dictionary.com:
Idioms & Phrases to beat the band
Also, to beat all. To the greatest possible degree. For example, The baby was crying to beat the band, or *The wind is blowing to beat the band , or *John is dressed up to beat all . This idiom uses beat in the sense of "surpass." The first term may, according to one theory, allude to a desire to arrive before the musicians who led a parade, so as to see the entire event. Another theory holds that it means "make more noise than (and thereby beat) a loud band." [Colloquial; late 1800s]
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: