ACR TAKES WRONG TXWY AT BWI AND CROSSES ACTIVE RWY.

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IT WAS NIGHT WITH RAIN SHOWERS IN THE VICINITY. WE PUSHED BACK FROM THE GATE FOR OUR FLT TO PVD AND WERE GIVEN CLRNC FROM GND CTL TO 'TAXI TO RWY 28; CROSS RWY 22.' BOTH THE CAPT AND I HAD OUR COMMERCIAL ARPT DIAGRAM PAGES IN FRONT OF US. WE WERE BOTH KEENLY AWARE OF THE LARGE AMOUNT OF RAMP CONSTRUCTION UNDERWAY AT BWI. AS WE TRAVELED S FROM THE GATE (W OF THE FIRE HOUSE) APCHING TXWY A; THE CAPT REPEATED THE TAXI CLRNC VERBALLY IN THE COCKPIT; 'TAXI TO RWY 28; CLRED TO CROSS.' I RESPONDED 'THAT'S CORRECT.' WE WERE NOW AT THE CONFLUENCE OF TXWYS A/P/E AND MISTAKENLY CROSSED RWY 28 AND TURNED L ON TXWY D VICE MAKING A L TURN ON TXWY P. UPON REACHING INTXN T; WE REALIZED OUR MISTAKE AND HAVING ALREADY SWITCHED TO TWR FREQ TOLD THEM OF OUR SIT AND LOCATION. THEY RESPONDED 'NO PROB; UPON REACHING THE APCH END YOU ARE CLRED FOR TKOF RWY 33L.' WE READ BACK THE CLRNC; AGAIN APOLOGIZED FOR OUR MISTAKE AND DEPARTED. I TRULY BELIEVE THE E/P/A INTXN JUST N OF RWY 28 TO BE A SIGNIFICANT HAZARD AS CURRENTLY MARKED. THE CONFUSION HERE IS COMPOUNDED BY THE ABUNDANT RAMP CONSTRUCTION NEARBY MARKED WITH AMBER FLASHING LIGHTS ON BARRIERS AND CONSTRUCTION BOUNDARIES. TWR/GND CTLED RED 'DO NOT CROSS' LIGHTS INSTALLED ON THE TXWY E HOLD SHORT LINE OF RWY 28 WOULD BE A GREAT SAFETY ENHANCEMENT AS WELL AS IN PAVEMENT GREEN LEAD-IN LIGHTS DIRECTING PLTS TO MAKE THE L TURN ONTO TXWY P. FROM DISCUSSING LESSONS LEARNED WITH THE CAPT; HE AND I HAVE DECIDED TO USE TXWY A TO TXWY C WHENEVER WE ARE ASSIGNED RWY 28 IN THE FUTURE. BWI MIGHT CONSIDER THIS FOR THEIR SOP UNTIL A SOLUTION TO THE HAZARDS AT THIS INTXN ARE PERMANENTLY PUT IN PLACE.