The site plan with the elevations for both the courthouse and office tower were posted to the AULCC page.
ftp://ftp.ci.austin.tx.us/ATD_AULCC/...F2_PLAN_01.pdf
They show the heights as 238 feet 6 inches to the mechanical penthouse for the commercial office tower with 13 floors, and 234 feet 6 inches for the courthouse with 12 floors.