Sierra Blanca, a complex ancient volcano, rises more than 7,300 feet above Tularosa Basin to peak at 12,003 feet. Vertical geologic movement between ranges and basin is about 2 miles. San Andres Mountains on the west side of Tularosa Basin are uplifted on east side and tilted westward. Elevation 4,670 feet.
Sierra Blanca is the highest mountain in southern New Mexico and the highest mountain in the state not located in the Sangre de Cristos. Sierra Blanca does have the highest prominence in the state. Prominence is the distance from the lowest point around the mountain to its highest peak. Its name means "White Mountain," and it is home to a popular ski destination known as "Ski Apache" which is run by the Mescalero Tribe.
I grew up 5 miles north of Carlsbad, and could see Sierra Blanca off in the distance from my front yard, although it was a 150 mile drive away (not as the bird flies of course).
I didn't have to refer to any sources outside of Wikipedia (to get a few statistics and other facts).