Sounds like an old 3208. As for the white smoke, does it smell really rich and burn your eyes? Your injectors may be dirty and not atomizing the fuel. The effect will be worse when the engine is cold.

Also, it could be caused by the ultra-low sulfur fuel we now have. The process used to remove the sulfur content also removes the lubricating properties from the fuel. This can cause premature wear in the injection pump and nozzles. I would run some really good fuel conditioner through it. I use Stanadyne fuel treatment in mine.

I am a heavy equipment mechanic, and one of my customers called me one day because he couldn't keep his diesel forklift running. When I got there, I checked the obvious, fuel filters, air filters, water in the fuel, etc. Everything looked OK. I asked him if he had been running fuel conditioner, and he said no. I gave it a heavy dose of Stanadyne and got it started. After about 20-30 minutes working the throttle, it smoothed out and ran fine.

What I mean by working the throttle is get it running, then throttle it up and let it idle down. Keep repeating this process for a little while. That will give the pumping mechanisms an other moving parts time to get lubricated.