I recommend that you approach the tower in Burnley from the South. Ignore the enemies occupying the balcony above and use the detective vision to locate the window shown in the above screenshot. Unlock your passage by using, of course, the explosive gel.
Jump inside and use the Cryptographic sequencer on the control panel on the left, which will result in determining the password shown in the above screenshot.
Use the claw now, to rip off the venting shaft grate below the ceiling. After you succeed, use the hook to grab onto the shaft and follow the venting shaft.
NOTE- If Batman does not want to climb into the shat, this means that you have fallen victim to one of the more serious glitches in the game. In such a situation, try installing the most recent patch or find out, e.g. on the You Tube, about a smart way to take advantage of another glitch in the game (Batman Arkham Origins Burnley glitch fix), thanks to which the Batman will land on the rooftop and will be able to activate the comms tower.
After you reach the shaft's final part, force the grate open, as a result of which you will reach the rooftop of the building with the comms tower. Open the reinforced door, approach the console and use the Cryptographic sequencer again. Just like earlier, you need to determine the correct password (the screenshot).