back to the shop

could be worse could be on the side of the road and the temp was 10 below

 

Ok, what is the code? International has a really good after treatment diagnostic manual. They are obviously not following it. When was the last time the after treatment injector was removed and cleaned?

 

There are tests and checks they need to be doing with the engine to make sure the engine is healthy and not running in a such a way that it makes extra soot. There are basic inspection points, good ECM powers and grounds, oil level, fuel quality, air to air leaks and so on. If there are problems here the engine can create more soot than what it is suppose to and plug up the dpf in no time. There are performance specs the engine needs to meet that are pretty clear to understand. They should be taking the truck for 0-60 mph performance snapshot and record it with the computer. Then after that perform an Air Management Test snapshot and record it. From these two tests you can get a ton of information on how the truck is running. You can see fuel rail pressure, intake manifold pressure, exhaust back pressure, DPF differential pressure, ECM voltage, soot load build up and so on. With the air management test you see if the egr valve is working properly, exhaust back pressure valve and turbo charger wastegate actuator are working properly. It is actually a nice system when you know how to work it. Have they done any of this?
As far as the forced regen goes, starting at 38% is weird. The warnings don't start until 80%. Forced regens end on their own around 20-27%. Once the engine cools down a bit and you go for a road test it will drop some more to some times 5%, but they usually bottom out around 15-20%. They never get to zero. I have seen DPFs that are just fully plugged from coolant ash. I think you said your egr cooler was replaced in another post. The coolant that leaks into the exhaust gets collected in the dpf as a vapor sort of, but still develops a crust chalky type of powder inside the DPF. This doesn't really burn away like fuel soot does. It takes nothing to plug up a DPF. I have seen DPFs regened down to 20%, road test the truck, and it is back up 80% 20 minutes later! DPF has to come out and be cleaned. When they clean DPFs and DOCs there is an air flow test they do before and after the cleaning. If the air flow is still creating too much back pressure that means the DPF is plugged beyond cleaning and must be replaced.
So they should be doing those other tests. I think pulling out the DPF would be wise and they should also run the engine with no exhaust connected to it and snap the throttle to see if it smokes excessively. Your truck also has a "Pre-DOC" which is a small DOC section right after the turbo. This should also be removed and inspected/washed out.