I had a similar problem with an '02 I just purchased this week, but mine did it at idle in the driveway. Found it was a fuel leak coming from the fuel filter outlet tube that's designed to drain water out of the fuel filter housing when your 'water in fuel' indicator light comes on. There is a little yellow handle on the right rear side of the fuel filter housing (left side when viewing from the front of the truck). It appeared to have walked partially open during operation, when I tried to moved it to the completely off position, it would kinda creep back...so...I built a bracket and hooked a small spring to the hole in the yellow handle to keep it from 'walking' open on its own...only 25 miles with this so far, we'll see if that fixes it for good.
Take the 'Powerstroke' plastic cover off the front of your engine so you can see the fuel filter at the front of the motor...look at the back side of the housing down low for the little yellow handle and check its position. Closed should be attained by moving the lever towards the passenger side of the truck...hope this helps.
Also, diesel will appear fairly clear on your finger, oil will be brownish or black.