You've been captures by a cutscene, placed in the custody of the Enclave and taken to Raven Rock.
At the first interrogation scene, follow any dialogue path until you get the option to provide the code. At that point, tell him you don't know the code, or that the code is 7-0-6. At this point, President Eden will recall Colonel Autumn and release you from the cell.
Alternatively, you can also tell him the code is 2-1-6 (the correct code) for an alternative cutscene in which he has his men at the purifier confirm this, before executing you.
On leaving the cell, you will be confronted by an enclave officer. Either intimidate him with Strength, or pass a Speech check to avoid combat. Take a right, and President Eden will announce that you are to reach the control room and not to be impeded.
Scavenge items as necessary — you have plenty of time to do so.
The closest exit is in the central area, in the north-west corner of the upper floor. The other exit allows you to avoid slightly more fighting in Sector 2, and it is located in the south-west corner of the level, behind the cafeteria.
Once you enter either room near the exit, the Colonel Autumn orders to ignore the president's directive and that you should be shot on sight.
Enclave soldiers are hostile and will engage as they see you. Their primary equipment is Power Armor and Plasma rifles.
Colonel Autumn's room is near the northwest corner of the floor, just south of the large rotunda to the control room. Aside from the energy bobble head, there is a ZAX destruct sequence that can be obtained within the quarters (Lockpick 50).
The exit is to the west of the rotunda.
The control room is guarded by Enclave soldiers and sentry bots. You quickly see the sentry bots use their laser weapony and cut the soldiers to shreads, and then state you can now see the president.
You are given a modified FEV virus to be placed within Project Purity.
With a high science or speech at 50%, you can convince President Eden that the base should be destroyed (after you take the FEV virus.)
The escape route is just beyond the door; head straight down the tunnel killing any opposition you encounter. If you want, you can collect a Gatling laser from a supply create, but it's in poor condition.
Return to Elder Lyons in the Citadel after you've escaped.