A321 First Officer reported a Low Brake Pressure EICAS message when setting the parking brake after a pushback; resulting in the aircraft moving on its own when the parking brake malfunctioned. The Captain activated setting the parking brake and no injury or damage occurred.

Narrative

Prior to pushback; the Captain was having issues with his communications with ground personnel. The Captain said he could not hear the ground person well and to be ready for hand signals but the ground person said he could hear OK and would speak loudly. I was communicating with ramp but also listening on the intercom at the time (on mute).We were cleared to push back from the gate and proceeded normally until the ground person said set brake". The Captain set the brake but then we got an EICAS message "Low Brake Pressure". He asked the ground person not to release the plane so he could reset the parking brake but apparently the ground person misunderstood and went ahead and released the plane. Meanwhile; as the Captain released the parking brake we got another EICAS message; "Low Accumulator Pressure"; which we both looked at as we thought we were secured. I then looked up and saw we were moving and as I announced that; Ramp called us and told us to stop moving backwards. I confirmed we were setting brakes as the Captain activated the Parking Brake. No further EICAS messages were noted."