This snake is in our yard, south of Deming NM, in Luna County. Approximate length is about 3 1/2 feet. It moved slowly at the time, but was being picked on by a couple of medium-sized birds. It is basically black with a black, narrow head. The body and snout have pale yellowish markings. On the body, the yellow is individual scales, so almost spotted. And on the snout, more like lines or stripes. I have some good photos, and even videos, but it says the files are too big - need to be under 2 giggleburps or something and I don't know how to do that.
Though a full body image would help a lot, I feel certain that it is the desert king snake scientifically known as Lampropeltis getula splendida. This species is seen in most parts of New Mexico and is not venomous. It primarily feeds on rodents, lizards, birds, snakes and eggs.
Here's a link to a website with more details on this species and other snake species of New Mexico: http://www.nmherpsociety.org/reptiles/snakes/lampropeltisgetulasplendida/index.html
Here's a variety of different photos of the desert king snake from different angles (but different ages, sizes and pattern varieties of the same species).