Fort bend county + parts of Harris will get you there fairly easily too.
I think this is harder than you think it is; do you care to demonstrate your solution? To get to 28% Asian/Hispanic/Black you need <16% white. For 30% you need <10% white. Are there enough precincts where Asians are a large majority but whites aren't a significant minority?
This doesn't perfectly adhere to your criteria, but it does have just 11% whites in 4th place with nearly twice as many Asians + whites still being 4th by CVAP.
