First off, you've got to (Sadly.) Do some Minuteman radiant quests, yes I know, Prestron Gravey is the worst person ever. Though, I don't know the specific number of quests, from my judge it's around, 3-5.



Upon doing so, Preston Gravey will talk about retaking the Castle, once iformed, you will gain the quest : Taking Independance, do the quest.

Congrats, you've unlocked the Castle.

I'm assuming that you've read the above, if not, read the thing.
First off, get to my reccomended level of, 15 - 25 next, if you have Automatron installed, build something powerful, you don't need the Minuteman Radiant Quests done for this moment, simply storm the castle all by yourself, the small Minuteman army is replaced with, your robot.
Once completed, get the quest, and your character will say something like : I've actually already stormed the castle all up in this shizzle.

Boom. You are done.

You all smell.