Strange smoking problem

The ECM can only detect electrical faults in that engine, not a mechanical misfire. If the engine starts fine, and this goes away once warm, I would also say it is an injector. If the engine is a bit stubborn to start or takes a bit longer cranking time to fire, the check valve at the back of the head may be allowing fuel to leak out of head.
As for injector testing, they should be able cut out injectors one by one even just after start up when cold to see which one makes the smoking stop to pin point the bad injector.

 

Fire the engine up cold and immediately jump out with an infrared thermometer, run around to the exhaust manifold and check the temp on each cylinder. The coldest one is going to be your culprit.

 

Another way is to run it with the exhaust manifold off. It will be very apparent which cylinder/s is smoking.

 

A good temp gun will be needed

 

The best temp gun is your hand.... but you have to be quick.

 

What color is the smoke?
I would be leaning towards valve seals or tiny crack in the head depends on smoke color.

My S60's typically smoked cuz of turbo seal leaks after long periods of idling. one was because of valve seals. Blue smoke is oil, black is fuel, white is coolant.
Also had one that had a bad head gasket where on startup would get tons of white grey smoke then it went away when warmed up. had a small crack in the head on #5 i changed out that cylinder all 6 injectors for the fun of it (they were old but not related to the problem)re did the head and gasket. problem went away. there was a build up of white crusty stuff on the head and piston (burnt coolant)

 

Running with the exhaust manifold is the best way. Many times, injectors fail by not seating, so even cutting the injector doesn't stop the fuel trickling out of it. You can usually find a bad one by running a cut-out test and comparing the #'s. You should run 3 tests and average the #'s. I also like to run it at idle and 1000 rpm. Any time I have injectors out, I pull a vacuum on the injector tip. A good injector will hold vacuum. I made up a short hose to a hand vacuum pump If the gauge creeps down, the tip is leaking.

Also check the cam really good, a lode going flat can also make smoke, which usually clears up when warm. You'd usually feel a miss though.

The parking brake thing isn't uncommon. There are parameters that allow 1/2 engine mode with the parking brakes set. If this is enabled, it can smoke less with the brakes set, since it's only running on 3 cylinders.