Armory can be found in the eastern part of level two of Psychotronics, next to the Extraction Lab. The area cannot be accessed, as the reinforced door (shown on the screenshot) is locked shut.
You can access the room in a few different ways. First method involves visiting the aforementioned Extraction Lab. Explore the lab to find Aaron Ingram, who is being held in a large glass cage. The man will ask Morgan to help him escape (The Prisoner in Psychotronics). You can agree and use the terminal nearby to open the cage. Aaron will give you the armory code (in our case, the code was 8714, but you may be left with a different combination) - use it to access the room.
Note - You can simply dispose of Ingram once you've received the code (in case you are aiming to eliminate all living personnel found on the station), or make an attempt to open the armory door on your own. Unfortunately, the door is protected by a level three lock, so you'll need Hacking III in order to access them.
Other than that, you can use one of the Typhoon powers to get access into the room. Check the requirements for Mimic Matter, an ability that allows you to pose as one of the objects found in the near vicinity. If you've managed to acquire the power, take a look at the corridor that neighbors the entrance to the armory. Approach the small window shown on the screenshot 1 and use the Wrench to clear the area from glue fragments leftover from a GLOO cannon burst.
Jump on a small windowsill, crouch, and use the Mimic Matter to transform yourself into one of the small objects found next to the window. Once you've managed to pose as one of the objects, get through a small window to enter the Armory.
Regardless of the chosen method of approach, investigate the arsenal thoroughfully. You'll find weapons and ammunition, an unused Turret, a Neuromod, Fabrication Plans for the Shotgun and 9mm Ammo and a Weapon Upgrade Kit.