Playing on Xbox 1
Lockpick the armory doors before picking up the final note on the ground to replicate.
Playing solo
1 player in session
Alright, if you lockpick all the armory doors before picking up the note next the dead soldier off the ground, you will bug the quest, preventing you from completing it as the next objective is to open the inner weapon storage. If you try to restart your game, the door for the armory will be locked regardless if the power is on or not.