The pass card found on the remains of the Vulkar lieutentants in the barracks of their base is just one of three ways to disarm the security turrets guarding the garage elevator: you can also shut down the garage elevator security system using the security panel against the north wall opposite the armory with sufficient Computer Spikes (maximum 8, -1 for every 4 Computer Use ranks), or enter Solo mode, open the door opposite the turrets and run back across the corridor to the opposite wall, then use grenades (preferably Ion Grenades) to kill the turrets from beyond their range (since they have On Hit: Instant Death), targeting the middle turret so that all three are within the area of effect.
However, your reference to the lower and upper level of the base suggests you've already used the elevator: are you looking for the garage head key card to open the security doors to the engine lab in the southeast corner of the garage? If so, it can be found in the garage head's desk in his office at the north end of the tunnel exiting the garage from its southwest corner.