The solution to your problem is quite simple. You've set the ISO far too high at ISO 12,800 and underexposed the shot. Combine the 2 factors and you will get noise.
There's no need of f14 and 1/4000 to capture a portrait shot. Either you or the camera exposed for the sky and not the subject. The meter reading needs to be off the face and had that been done, you would have shot at least 1.5 stops brighter and had a lot less noise. But even so, the ISO is still far too high. I wouldn't shoot above ISO 800 even in cloudy skies outside. Preferably ISO 200
See the histogram here and the 1.5 stop increase below. The "hump is all to the left and should be an even hump in the middle, or more to the right.
Now with the proper exposure on the face, you are really seeing the noise from using an ISO that's too high combined with a shot that's underexposed by 1.5-2 stops.