'Exotic' weapons are any weapons that are mounted on tripod. You can find a Heavy Bolter and a lot of Orks in Chapter 2 where you can grind it out, and there are Plasma Cannons on Chapters 4 and 7 or 8. Mounted Autocannons can also be found later in the campaign. These weapons can be ripped off of the turret mount to carry around during the Chapter. For most turrets this disables its infinite ammo.
To grind this out, simply go to Chapter Select under Single Player, select Act 1, Chapter 2, and the section labeled "Trenches". Play through the Chapter until you reach the Digga cutscene where Ork machines bust up through the ground into the Imperial Guard trenches, then continue around the next few corners until you see a mounted Heavy Bolter. This is the location you want, as you can net somewhere between 30 and 50 kills after grabbing the Heavy Bolter. Once you gun down the horde, simply reload the checkpoint, run back around the corner, and begin the process again.