D328 PIC DISCUSSES WITH BOS SUPVR THE CLRNC READBACK ERROR THAT IS BEING PROCESSED ON THE GND CTLR.

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WE HAD FLOWN AN ILS TO VISUAL CONDITIONS FOR RWY 4R AT BOS. AFTER LNDG WE CLRED THE RWY AT TXWY Y AND TURNED L AGAIN ON RWY 33R. DURING OUR ROLLOUT; WHILE WE WERE TRANSFERRING ACFT CTL FROM THE FO BACK TO THE CAPT; WE RECEIVED A TAXI CLRNC FROM THE TWR CTLR. MY FO AND I WERE BOTH SURE THAT WE WERE CLRED TO CROSS RWY 4L; TURN L ON TXWY N; AND CONTACT GND CTL. THE FO READ BACK 'CLR TO CROSS 4L.' THE TWR CTLR DID NOT CORRECT THIS READBACK OR CHALLENGE US. IN THE ABSENCE OF A CORRECTION AFTER THE READBACK; WE CROSSED RWY 4L IN ACCORDANCE WITH ESTABLISHED PRACTICE. I HAD CHKED TO MY L PRIOR TO CROSSING RWY 4L; AN DID NOT SEE ANY ACFT ON THAT RWY. WHEN WE CONTACTED GND CTL; WE WERE GIVEN A TAXI CLRNC; AND TOLD TO CONTACT THE TWR SUPVR WHEN WE GOT IN. THE TWR SUPVR TOLD ME THAT WE HAD BEEN TOLD TO HOLD SHORT OF RWY 4L; AND THEY WERE LISTENING TO THE TAPES. THE TWR SUPVR TOLD ME THEY WERE PROCESSING AN OPDEV ON THE TWR CTLR FOR NOT CORRECTING OUR 'CLRED TO CROSS' READBACK. I FEEL THE ROOT CAUSE OF THIS INCIDENT WAS THE ISSUE OF A CRITICAL CLRNC DURING ONE OF THE MOST CRITICAL PHASES OF FLT. OUR CONCENTRATION WAS PRIMARILY ON FLYING THE ACFT DOWN TO TAXI SPEED; AND EXITING THE RWY.