You can attempt this quest when you’re a bit high leveled with better skills, perks, and equipment. Once done, you can talk to Preston Garvey about taking over The Castle. Head to the Castle’s location in Southern Boston and meet up with Garvey and three more minutement in the ruined diner. Talk to him and you’ll have to decide on one of the three suggested plans of attack: attack with guns blazing, draw them out, or set up a pincer attack.
Whatever plan of attack you decided on, clear the razorclaws in the courtyard then proceed in taking/destroying all eggs in the nests in the courtyard and on the walls. After destroying enough, the Mirelurk Queen will appear. Use your best guns and don’t hesitate to pop multiple chems if needed.
After defeating the queen, you have to activate the workshop and Power up the transmitter. It requires 10 power alone so you have to build a large generator to power it up. Once done, you can talk to Garvey to complete the quest and you’ll be able to set The Castle up as your workshop.