The weakened Railroad needs an edge over the Institute. This can come in the form of Patriot, their covert Institute contact. Unfortunately, they've only been able to receive messages from him and couldn't send any out. It is up to the Sole Survivor to arrange that...
Use the tape on any terminal in the Institute. Contact Patriot.
Follow the map marker to the closet under Advanced Systems (accessed through the mezzanine). Talk to Liam Binet about his plans.
Follow him to Z1-14. Discuss the matter and agree to get the credentials for Code Defender.
Travel to the Railroad HQ. Talk to Desdemona and input the report on the terminal in PAM's room.
Talk to PAM to learn the location of the credentials. Travel to Cambridge Polymer Labs and find the terminal in the laboratories. Complete the side quest to get out.
Travel to Railroad HQ and talk to Desdemona. She thinks big, doesn't she?
Travel back to Liam Binet and give him the code. Then talk to Z1-14 about the mass uprising.
Wait 24 hours and return to Z1. He needs weapons. Deposit any you want in the closet opposite Liam's meeting place, in the wooden footlocker.
Travel to the elevator between Robotics and the SRB. Take it down below.
Kill the guards. Note that one hit kills may cause the quest to bug out and turn the Institute hostile.
Upload encrypted message on any Institute terminal
Desdemona gave me an encoded holotape that I can use at any Institute terminal to make contact with the Railroad's guardian angel, Patriot. Perhaps with him (or her) we can devise a way to rescue many synths.
Read Patriot's reply
Meet Patriot
Tinker Tom's encoded holotape worked. I sent an encrypted message to Patriot and received a message back: "Meet at the Advanced Systems maintenance room."
Follow Liam
I've met Patriot, Liam Binet. He's eager to rescue a lot of Synths at once. But in order to do that we'll need help. I should follow Liam to meet his accomplice.
Talk to Desdemona
Patriot has a plan to rescue 13 Synths at once. But he needs login credentials for CIT's original security system, Code Defender, to do so. I should contact Desdemona to find them.