CHECK AIRMAN AND IN TRAINING CAPT ON EARLY MORNING FLT TO A CLOSED TWR ARPT ABOARD B767-300 FORGET ABOUT CLOSED TXWY AND ARE UNABLE TO COMPLETELY EXIT THE RWY DUE TO BARRIERS.

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WE ARRIVED AT THE ZZZ1 GATEWAY AND REVIEWED THE PAPERWORK FOR THE FLT FROM ZZZ1-ZZZ. AFTER A SHORT LAYOVER IN ZZZ; WE WERE TO CONTINUE FROM ZZZ TO ZZZ2. I WAS CONDUCTING TRAINING FOR A CAPT THAT WOULD BE AN OE INSTRUCTOR FOR OVERWATER STUDENTS. WE HAD BEEN DISCUSSING VARIOUS OVERWATER ISSUES ON THE RIDE OUT TO THE GATEWAY; AND WHEN WE RECEIVED OUR PAPERWORK; WE ONLY HAD THE FIRST LEG TO ZZZ NOT ON TO ZZZ2. OUR LAYOVER IN ZZZ WAS ONLY FOR APPROX 1.5 HRS. SINCE THE LAYOVER IN ZZZ WAS SO SHORT; WE DECIDED TO GET THE OTHER FLT INFO FOR THE NEXT LEG. THE CAPT IN TRAINING WANTED TO DISCUSS SOME OF THE INFO FOR THAT LEG; AND ASK SOME QUESTIONS. I MUST ADMIT I WAS TIRED; AND HAD NOT SLEPT WELL BEFORE THE FLT; AS I WAS HAVING SOME SEVERE PAIN WITH A TOOTHACHE; SO I WAS NOT RESTED. I HAD NOT BEEN TO ZZZ AND THE CAPT IN TRAINING HAD BEEN THERE MANY TIMES. WE DISCUSSED THE SHORT RWY; THE APCH AND LOOKED AT THE WX. I REVIEWED THE NOTAMS; AND SAW A NOTE ON THE DEP WE WOULD BE DOING OUT OF ZZZ FOR THE ZZZ2 LEG; AND THE RWY AND TXWY CLOSURES. I KNEW RWY WAS NOT A PLAYER SINCE IT WAS SHORT; AND THE TXWY CLOSURE WAS REVIEWED. IT DIDN'T STICK WITH ME HOWEVER. WE WENT TO THE AIRPLANE AND DISCUSSED MORE OVERWATER INFO AND FMC QUESTIONS. WE DID A SINGLE ENG TAXI; WHICH THE CAPT IN THE FO SEAT HAD NOT DONE FROM THAT POS. THE TKOF; CLB AND CRUISE WAS NOT A PROB. DURING THE APCH BRIEF; THE PF MENTIONED THAT WE WOULD TURN OFF TO THE L AND TAXI BACK. I COMPLETELY FORGOT THE NOTAM ABOUT THE TXWY CLOSURES. IT DID NOT OCCUR TO HIM EITHER. NOTHING SERIOUS MENTIONED. I WAS THE PM (PLT MONITORING) AND LISTENED TO THE ASOS; AND NOTED THE WX AND THAT THE TWR WAS CLOSED; BUT NO MENTION OF RWYS OR TXWY CLOSURE. ON APCH THE PLT CTL LIGHTS WERE ACTIVATED AT ABOUT 10 MI OUT. I ACTIVATED THEM AGAIN WHEN ABOUT 3 MI OUT AND THEY CAME UP ON A HIGH INTENSITY. THE CAPT STUDENT HAD TOLD ME HE WAS GOING TO TRY TO LAND CLOSE TO THE END OF THE RWY; IN THE TOUCHDOWN ZONE AS THE RWY IS SHORT; 5900 FT. HE FLOATED A BIT; NOT BAD; AND WE LANDED OK. HE USED AUTOBRAKES; AND THEN APPLIED THE BRAKES AND WE SLOWED; BUT WERE APCHING THE END OF THE RWY; SO I TOOK THE AIRPLANE APPLYING THE BRAKES TO AROUND 15 KTS WHEN I STARTED TO TURN TO THE L; FOR TXWY A. THIS TXWY; TXWY A; HAD ALL THE TXWY LIGHTS UP BRIGHT. WHEN I LEFT THE CTRLINE TO START TO THE TXWY; I NOTICED THE DIMLY LIT RED BARRICADES ACROSS TXWY A. I THEN REALIZED WE WERE ENTERING THE CLOSED AREA; BUT WAS UNABLE TO DO ANYTHING BUT STOP. WE HAD NOT EXITED THE RWY; BUT IT WAS TOO TIGHT TO DO ANYTHING. I WOULD GUESS OUR NOSEWHEEL WAS PROBABLY CLOSE TO THE LINE BTWN THE RWY AND THE TXWY. WE CALLED THE CTL FACILITY AND TOLD THEM WE WERE STILL ON THE RWY AT THE END; AND COULD NOT TURN AROUND. WE CALLED THE GATEWAY AND HAD THEM COME AND PUSH US BACK AND WE THEN BACK TAXIED DOWN RWY TO OUR PARKING AREA. IRONICALLY A FRIEND OF MINE HAD JUST FLOWN IN TO ZZZ THE WEEK BEFORE AND ALMOST GOT CAUGHT LIKE WE DID. HE MANAGED TO TURN AT THE END AND USE THE PORTION OF RWY THAT WAS NOT CLOSED TO BACK TAXI ONTO RWY AND PARKING. I SEE A COUPLE OF ISSUES HERE. 1) I DID NOT SPEND ENOUGH TIME ON THE NOTAMS AND SHOULD HAVE MADE NOTE OF THE SERIOUSNESS OF THIS OP RESTR; ESPECIALLY SINCE I HAD NOT BEEN HERE BEFORE. I BELIEVE BOTH OF US DURING OUR BRIEFING WERE MORE CONCERNED WITH THE OVERWATER PORTION OF OUR FLTS THAN THE SHORT FLT OVER TO ZZZ. IT WAS MY FAULT FOR NOT GIVING MORE ATTN TO THIS NOTAM AND ESPECIALLY SINCE A FRIEND OF MINE HAD TOLD ME OF EARLIER. IF WE HAD NOTICED THIS AND MADE IT A BIGGER ISSUE; WE COULD HAVE AVOIDED THE ISSUE. WE CERTAINLY HAD TIME TO NOTICE IT DURING THE PREFLT. MY FAULT. 2) THERE SHOULD BE A REMINDER ON THE ASOS; IF IT IS POSSIBLE; TO NOTIFY AIRMAN OF THIS ISSUE. I REALIZE IT IS ONLY A SHORT FLT FOR US; BUT NO MEMORY JOGGER FOR TIRED PLTS. FOR MOST OF THE ACFT THAT USE THIS FIELD; A 180 DEG TURN ON THE RWY IS NOT A PROB. HAD I BEEN IN A B757 I THINK I PROBABLY COULD HAVE MADE THE TURN. NOT SO ON THE B767. 3) WHY ARE THE TXWY A LIGHTS ON THE N SIDE OF RWY 5 TURNED ON IF THAT PORTION IS CLOSED? WHY CAN'T THEY BE TURNED OFF? ALSO; THE BARRIER LIGHTS TO PREVENT GOING DOWN TXWY A FROM RWY 2 ARE NOT VERY BRIGHT AND NOT NOTICEABLE UNTIL YOU GET DOWN TO THEM; IT WAS NOT NOTED UNTIL IT WAS TOO LATE AND THEN THERE WAS AN ISSUE. WITH THE TXWY LIGHTS UP BRIGHT; THE BARRIER LIGHTS WERE NOT TOO NOTICEABLE UNTIL IT WAS TOO LATE. WITH THE B767; IF YOU STAY ON THE CTRLINE TILL THE END; ONCE YOU LEAVE THE CTRLINE OF THE RWY; YOU ARE COMMITTED. IF YOU AREN'T PULLING OVER TO GET THE MAINS OVER TO THE SIDE FOR THE 180 DEG TURN; I BELIEVE YOU COULD HAVE A SERIOUS PROB TURNING THE AIRPLANE AROUND. I DID NOT WANT TO TRY TO MAKE THE TURN ONCE I LEFT THE CTRLINE FOR FEAR OF GETTING ONE OF THE MAIN GEAR OFF OF THE HARD SURFACE. IT COST US SOME TIME; AND FORTUNATELY WE WERE THE ONLY TFC AT THE FIELD. WE HAD THE RWY SHUT DOWN FOR ABOUT 10-15 MINS. CTL FACILITY DIDN'T SEEM TO BE TOO CONCERNED; AND WE KEPT THEM APPRISED OF OUR SITUATION. WE ALSO BROADCAST ON THE CTAF THAT WE WERE ON THE RWY. IT ALL BOILS DOWN TO ME NOT BEING VIGILANT ENOUGH ON PREFLT AND REVIEWING THE NOTAMS. HAD I DONE A BETTER JOB OF THIS; NONE OF THIS WOULD HAVE HAPPENED TO US. HOWEVER; I BELIEVE IF IT CAN HAPPEN TO ME; IT CAN HAPPEN TO ANYONE.