A B737 CREW TAXIING FOR TKOF AT BWI; BECAME DISORIENTED AND TAXIED ACROSS AN ACTIVE RWY WITHOUT A CLRNC.

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BWI -- CLRED TO TAXI FOR TKOF RWY 28. I MADE A WRONG TURN AND CROSSED RWY 28 WITHOUT CLRNC. THERE WAS NO TFC CONFLICT WITH OTHER ACFT. GND CTL TOLD US TO TURN AND CLRED US BACK ACROSS RWY 28. I LOOKED BOTH WAYS BEFORE XING AND SAW NO TFC; BUT THOUGHT I WAS XING RWY 4/22. WHAT MOST CONCERNED ME ABOUT MY ERROR WAS THE FACT THAT I THOUGHT I WAS BEING CAUTIOUS. I HAD THE ARPT DIAGRAM OUT AND IN FRONT OF ME. THE FO HAD THE PERFORMANCE DATA FINISHED; BUT I SAID I WOULD LOOK AT THE DATA AFTER TAXIING PAST THE INTXNS. THE FO WAS NEW (THIRD TRIP) AND NOT FAMILIAR WITH BWI. I THOUGHT I WAS BEING CAREFUL; BUT STILL MADE THIS MISTAKE. WE WERE NOT RUNNING CHKLISTS OR LOOKING AT PERFORMANCE COMPUTER AND THERE WERE NO OTHER DISTRACTIONS. I CANNOT DEFINE ANY FACTORS THAT CONTRIBUTED TO MY ERROR EXCEPT MY MENTAL DISORIENTATION WHILE TAXIING OUT. SUPPLEMENTAL INFO FROM ACN 533506: FLT WAS CLRED TO TAXI TO RWY 28 FOR DEP. WE PROCEEDED FROM GATE X TO TXWY E. PROCEEDED ACROSS RWY 10/28 AND WAS QUERIED BY GND CTLR. GND CTLR THEN CLRED US TO TXWY D AND ENTRANCE ONTO RWY 4 TO TAXI BACK ACROSS RWY 10/28. WE TAXIED RWY 28 AND DEPARTED. WE LANDED ON RWY 33L AND TFC WAS LNDG ON RWY 33L AS WE TAXIED. CAPT MAY HAVE CONFUSED LNDG RWY WITH DEP RWY? IF I HAD BEEN MORE FAMILIAR; I WOULD HAVE QUESTIONED THE TAXI RTE THE CAPT WAS TAKING. LESSON LEARNED: AS A NEW FO; AND FROM NOW ON; I WILL BE MORE DILIGENT IN MONITORING TAXI RTE. AT UNFAMILIAR ARPTS; I WILL ASK CAPT TO CONFIRM TAXI RTE.