ACR CREW FLIES THE PROC FOR THE INCORRECT RWY ON THE BOSTON LOGAN 2 DEP.

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BOSTON WAS DEPARTING RWY 9. ONCE PAPERWORK WAS RECEIVED PRIOR TO DEP; WE DECIDED WE WOULD REQUEST A LONGER RWY FOR DEP DUE TO ACFT WT. WE WEREN'T SURE WE WOULD RECEIVE A DIFFERENT RWY THAN RWY 9; HOWEVER; DUE TO THE BUSY NATURE OF THE BOSTON ARPT AT THE TIME; WE CONTINUED TO PLAN A RWY 9 DEP. THE LOGAN 2 DEP FOR RWY 9 IS SIMPLY TO FLY THE RWY HDG. WHILE TAXIING OUT; THE TXWYS WERE QUITE CONGESTED AND A LOT OF ATTN WAS GIVEN TO TAXI OPS. DURING TAXI; BOSTON APPROVED OUR TKOF ON RWY 4R. MY COPLT MADE APPROPRIATE CHANGES TO THE FMS AND AUTOPLT CTL PANEL. ONCE WE GOT TO THE RWY; OUR DELAY FOR TKOF WAS BRIEF AND I DID NOT BRIEF ANY ADDITIONAL CHANGES TO THE DEP. THE RWY 4 INSTRUCTIONS INDICATE TO TURN TO 090 DEG HDG AT 4 DME. NAVAIDS WERE SET BUT AFTER TKOF I DIDN'T TURN AT 4 DME AND THE CTLR GAVE US A TURN AT ABOUT 6-7 DME; AND STATED 'FOR FUTURE REF WE SHOULD TURN AT 4 DME.' THE VECTOR GIVEN TO US WAS 120 DEGS. MY COPLT MISUNDERSTOOD AND PLACED 210 DEGS IN HDG WINDOW. I WAS HAND FLYING AND ONCE THE TURN STARTED; I TURNED ON THE AUTOPLT AND FAILED TO NOTICE THE HDG ERROR. THE ACFT TURNED PAST 120 DEGS AND THE CTLR RESTATED OUR HDG SHOULD BE 120 DEGS. I CORRECTED THE HDG. THERE WAS NO MENTION OF TFC CONFLICTS BY THE CTLR. THIS SIT DEVELOPED AS A RESULT OF SEVERAL SEQUENCES OF EVENTS. PREFLT PLANNING WAS INCOMPLETE DUE TO CHANGES IN RWY FOR DEP TAKING PLACE DURING A VERY ACTIVE PERIOD DURING TAXI OUT. THIS WAS FOLLOWED BY LITTLE TIME TO PREPARE FOR CHANGES TO DEP INSTRUCTIONS NOTED ON THE SID. FAILURE ON MY PART TO TAKE THE ADDITIONAL TIME TO REVIEW THE SID THOROUGHLY. AFTER AIRBORNE; THE COPLT DIALED IN THE WRONG HDG; BUT I FAILED TO DOUBLECHK HIS FINAL HDG SELECTION. TO AVOID FUTURE OCCURRENCES; I PLAN TO TRY TO GET RWY CHANGE REQUESTS TAKEN CARE OF BEFORE TAXI HAS BEGUN. AUTOMATION COULD HELP IF THE LOGAN 2 DEP WAS IN THE FMS DATABASE AND WOULD HAVE THE TURN PROGRAMMED. OBVIOUSLY; DOUBLECHKING THE INPUT OF THE PNF IS ALWAYS NECESSARY BY THE PF. THE FIRST ERROR OF MISSING THE TURN PROBABLY CONTRIBUTED TO THE SECOND ERROR OF THE WRONG HDG GOING UNCORRECTED; SINCE I HAD SELECTED AUTOPLT AND WAS THEN CHKING THE SID INSTRUCTIONS TO SEE WHERE I HAD MISSED THE TURN; THEREFORE; NOT PROVIDING FULL ATTN TO THE COPLT'S FINAL HDG SELECTION UNTIL PAST THE DESIRED HDG.