This is given by Father after completing the quest “Institutionalized”. Head to the marked location (Nahant Wharf) and meet up with the courser, X6-88. When meeting up with X6-88, he may come under attack from a Brotherhood of Steel team and a Vertibird. Since he is tagged as an essential character, he won't die. The BoS members attacking him may cease hostilities when he's down. If you're allied with the BoS, they won't attack you; so the best way to approach Libertalia is from the Nordhagen Beach side. You can fast-travel there and X6-88 will still be with you.
The target is in Libertalia, in the top floor of the main raider headquarters. You have to use the trapdoor on the ceiling to reach the rooftop area. You can use the recall code immediately on Gabriel or you can take the loot and let him walk away. Once resolved, return to the Institute and return to Father. You'll receive your own quarters. X6-88 will also inform you that Father is looking for you.