Sounds like the injector pressure sensor(ICP). They are a VERY common failure item on the 6.0, but are a pain to get to.
The quickest way to tell they are bad is to check and see if there is oil leaking out through the connector. If is real bad you can see it without taking any thing apart.
On the "early build" the sensor is mounted directly behind the turbo, beneath the "Y" pipe.
Crawl under the truck armed with a flashlight and a mirror that you can get into tight spots. From the bottom side of the truck there will be a heat shield that it hides behind, but with your mirror you should be able to get a glimpse of it. The wire that plugs into the sensor has a reflective heat shield on it also, but you should still be able to see a leak or wetness around the sensor or wire.
If you want to get a look at it from the topside you will have to pull your degass bottle, air cleaner, and ficm. With those out of the way you can squeeze your hand back there and slide the heat protector back from the connector and gently pry the locking tab back and pop the connector off.
If the leak is bad enough the hot oil will melt the connector and you must replace that also.
Also note that if this sensor is failing it will not always set a CEL or store a code in the PCM.
Here's a pic....
If your is the "late build" then its REALLY easy to get at. It is located on the right hand valve cover and looks like.........
Good Luck