FLT CREW REPORTS RWY INCURSION AT TEB AFTER LATE ARRIVAL AND QUICK TURN FOR DEPARTURE.

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WE ARRIVED LATE AT XA58Z WITH A QUICK TURN. OUR TIME ON THE GND IN TEB WAS 31 MINS. WE CALLED TEB GND FOR TAXI AND WERE GIVEN L ON TXWY L; R ON TXWY Q CROSS RWY 19 HOLD SHORT RWY 24. NO PAX ONBOARD AND WE WERE REPOSITIONING FOR MAINT FAR 91. IT WAS VERY DARK OUT WITH CLR SKY. WE WERE BOTH TIRED. MY COPLT HAD THE TAXI CHART OPEN. WE WERE APCHING A RWY AND THERE WERE NUMEROUS BARRICADES WITH YELLOW FLASHING LIGHTS OFF MY L WING WHICH WAS DISTRACTING MY ATTN AT THE CORNER OF TXWY L AND RWY 24. I ASKED MY COPLT FOR DIRECTIONS AT THIS POINT 'STRAIGHT AHEAD' HE RESPONDED 'YES.' I CLRED BOTH APCH AND DEP ENDS BEFORE XING AND REALIZED I HAD CROSSED RWY 24 WHICH I BELIEVED TO BE RWY 19. THE BARRICADES WERE IN THE IMMEDIATE VICINITY OF RWY 24 AND I MISSED THE RWY 24 SIGN BY THIS DISTR. MY COPLT SAID HE PUT HIS HEAD BACK INTO THE COCKPIT AND MISSED TXWY Q. I DID NOT SEE TXWY Q ON MY SIDE OF THE ACFT. THERE WERE NO ACFT ON THIS RWY AT THE TIME AND NO ACFT ON FINAL AT THIS TIME. THERE WERE NO CONFLICTS AT ALL AT THIS TIME. WE CALLED THE TWR AND ASKED IF WE PASSED TXWY Q AND THEY SAID YES AND TO CONTINUE TAXI TXWY L; R ON TXWY A HOLD SHORT RWY 24. I BELIEVE THAT THIS COULD HAVE BEEN AVOIDED IF A BETTER CRM ON THE BRIEFING OF THE TAXI CHART HAD BEEN USED AND BETTER LIGHTED SIGNS WERE MORE VISIBLE. THE BARRICADES NEAR TXWY Q WERE DISTRACTING TO THE CAPT AND NOT SURE OF THEIR PURPOSE AS THERE WERE NO TXWY TO BE BLOCKED. SUPPLEMENTAL INFO FROM ACN 793334: I SHOULD HAVE BEEN HEADS UP; EYES OUTSIDE DURING TAXI NOT FIXATED ON THE CHKLIST. AT THIS POINT I HAD 5.5 HRS; BEEN ON DUTY 9 HRS WITH POOR SLEEP THE PREVIOUS NIGHT.