If you're allied with other factions and requested the help of either the Minutemen (Sturges) or BoS (Ingram) in building the teleporter in the main quest “The Molecular Level), you can talk to Desdemona and agree to help the Railroad to unlock this quest. If you haven't surrendered the Network Scanner holotape to Sturges or Ingram, you can give it to Tinker Tom instead.
After handing over the tape, travel back to The Institute and load the Network Scanner on any terminal. Copy the encrypted message then wait for the Patriot's reply. Once done, follow the quest marker as it leads you to Liam Binet. After talking to him, follow him to the West Atrium. After talking a bit, Liam will tell you that he needs some old credentials for the next step.
Teleport to the Railroad HQ and talk to Desdemona. Next, head to PAM's room and load the report on the terminal. Talk to PAM then travel to Cambridge Polymer Labs. Head inside the lab and find Bergman's terminal in the second floor to the west. (Refer to Cambridge Polymer Labs' location page for more details)
Report back to Desdemona then travel back again to The Institute and talk to Z1-14 first. Next, hand over the password to Liam. Now you have to wait for 24 hours then talk to Z1 again. Once the plan is updated, head to the maintenance tunnel by following the quest marker then proceed in killing the synth guards. The nearby friendly synths will join the attack as well. Once done, talk to Z1. This quest will then be put on hold until you get the Institute quest Powering Up is completed.
Once the meeting has concluded in the quest “Powering Up”, a synth messenger will arrive and talk to you in a coded message. Find Z1-14 and talk to him to learn about the latest intel. Head back to the Railroad HQ and warn Desdemona. Once done, this quest will be completed and you'll reside a Railroad Rifle. The next quest will become available.