Wheeler Peak (13,161') is the New Mexico high point. There seem to be a couple of main routes: Bull of the Woods and from the Williams Lake TH. The Bull of the Woods route has a Strava segment (ascent only), which records the FKTs as far as we know.
Another possibility is the "Wheeler-Kachina Traverse" (submitted by Tyler King):
This is a 16.5 mile route in the Taos Ski Valley area with 6k feet of gain. From the main parking lot sign, follow the single track to ascend the Bull of the Woods Trail and summit Frazer Mountain, and Mount Walter on the way to summiting Wheeler Peak. The summit of Frazer is to the right of the main trail so don't forget that. From Wheeler, traverse to Simpson and take in the view of the work to come. Stick to the ridge line as much as possible while going up and over points 12,728 and 12,819 on your way to Lake Fork Peak. Traverse to Kachina while summiting point 12,535 on the way. After point 12,535 there is a short headwall which is class 4 if climbing straight down it or to the left looked like a loose gulley. Sticking with my goals of scrambling most of the way, I went straight down the headwall. Summit Kachina and look back at your accomplishment. There are 3 ways to descend Kachina that I saw or read about. Choose Main Street, Cabin Chute, or Lift Shack Chute. I'm pretty sure I went down Cabin Chute which was slippery with tundra. Then pick your way down with service roads to get to the Williams Lake TH. From here, finish off your legs by running down Twining Road back to the finish and tag the parking lot TH sign.
Sean O'Roarke reported some early speed ascents:
"Leafing through Herbert Ungnade's classic Guide to the New Mexico Mountains (1965), I happened to find a short section on "Climbing Records":
Charles Floading made the Wheeler Peak climb by way of Bull of the Woods Mountain in 2 hrs., 11 min., 20 sec., while Dean Rickerson climbed by way of Williams Lake in 1 hr., 8 min. Dean Rickerson also holds the speed record for the climb of West Truchas from the boundary fence at the irrigation canal. His time in August, 1964, was 1 hr."
Dave Dunham reported doing a logical, 14 mile loop using these 2 routes:
Eric Morse and I completed the Williams Lake, Wheeler, Walter, Frazer, Bull of the woods, loop this weekend (08/29/15) in 4:15:12.
Link to GPS = connect.garmin.com/activity/881712002
Link to blog post = ddmountainrunr.blogspot.com/2015/09/wheeler-peak-nm-state-high-point.html
What? Dist Time Climb
To Williams TH 2 0:25:13 769
To 67 1.6 0:31:38 935
To coll 2.1 0:51:08 1908
To Wheeler 0.3 0:06:06 110
On top 0 0:10:09 0
To coll 0.3 0:06:10 -110
To Walter 0.1 0:02:36 82
To La Cal 1.9 -1390
To Frazer 1.1 0:54:13 420
To Bull 1.4 0:24:34 -650/86
To car 3.3 0:43:25 -2161
Total 14.1 4:15:12