Without spoiling the game, you need to progress through the main quest until you reach a location called "the institute", once here you will be able to purchase the gun from a vendor, his name is synth ;) and he is off of one the paths from the center of the institute. He sells you the weapon, I have forgotten the price, I wanna say around 2000 caps.

Plasma rifle, 25% fire rate 15% reload speed

Here is where to find the institute
[ Register or Signin to view external links. ]

Here is a video