Once you have gone around and collected all the parts required for your buggie in Mission 3 - The Missing Part, instead of heading off to the right to exit, turn around and walk up the stairs.

There is a red Quake button hidden below the furniture on each of the 2nd, 3rd and 4th floors. The button is at the bottom of each wall near the floor. Go to each of the floors and press the button, when you do it you will hear a sound effect.

When you have done all three buttons, then go back to the 2nd floor and look for the red Quake symbol next to the stairs. You will now be able to walk up the stairs at the top of which you'll find a portal door that takes you to the hidden Quake room. You can also pick up the Shambler Plush item from the floor in the room.