Go to the Boeing website and search for "D6-58326-1". This document provides airport planning data for Boeing products.
An elevation of 1276ft for this airport appears to be right at the threshold of the 744's capabilities for MTOW (with the runway length you provide) per D6
So legally - I guess I'd have to extrapolate some data to see where this answer falls..... From the theoretical/technical perspective I'd expect the a/c to make it without trouble provided no problems arose (requiring rejected takeoff, etc). Of course the answer depends on ambient conditions and engine type as well.
I am not a pilot.