You get the weapon at the end of the second (and last) DLC story mission. You then unlock a challenge that you can use to fully upgrade the mods of the gun. This is needed I think.
What you have to do is kill 10 enemies in one firing of the weapon. So find a base with enemies grouped up and hold
to fire at them. Do not let go of the fire button and aim around trying to get all enemies.
If you fail then you can liberate the base and try again. You have to have completed the story to liberate a base. If you haven't then you can try this during a mission or on any bases you have available. I would choose a small base as I tried on the bigger ones, but found the enemies spread too far apart. I used "Guardia Val De Mar V" on the third island to get this.
I made a video of the moment I got this: