This large state is 400 miles west of Denver CO?
That would be Montana, however the distance in road miles is longer than 400 miles to the southern border of the state.
1928 miles taking this route: Take I-80 WEST to I-76 SOUTH to DENVER at EXIT 102 in Nebraska. Take I-76 to E-470 (tollway) SOUTH to LIMON. Take E-470 35 miles around Denver to I-25 to COLO. SPRINGS and DENVER. You are looking for I-25 SOUTH to COLO. SPRINGS. Take I-25 SOUTH to I-10 WEST to DEMING at END I-25 in Las Cruces, New Mexico. Take I-10 WEST to Tucson.