B737 CREW TAXIED OVER BARRIER ON A CLOSED TXWY AT TPA.

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ON ATIS NOTICED THAT TXWY A14 WAS CLOSED. THIS IS A VERY SHORT TXWY CONNECTOR. TRIED TO FIND A14 ON ARPT DIAGRAM; BUT COULDN'T FIND IT EASILY BECAUSE OF DARK CONDITIONS AND THE SMALL PRINTING ON THE PAGE. I ASSUMED THAT WE WOULD NOTICE IT BECAUSE THEY ARE USUALLY BLOCKED BY BRIGHT AND LIGHTED SAWHORSE TYPE BARRICADES. CALLED TWR FOR TAXI (CTLR WAS DOING GND AND TWR FUNCTIONS ON THE TWR FREQ); WAS CLRED FOR TAXI TO RWY 36R WITH NO ROUTING OFFERED. TAXIED ON MOST DIRECT RTE TO THE RWY WHICH HAPPENED TO BE TXWY A14. NOTICED NO BARRIERS; AND FELT NO BUMPS ON TAXI OUT. ENRTE ATC NOTIFIED US THAT WE MAY HAVE RUN OVER A BARRIER IN TPA. UPON LNDG; I WAS NOTIFIED THAT THE TXWY WAS CLOSED AT ACR'S REQUEST BECAUSE OF ITS CLOSE PROX TO ACFT PARKING AREA. THERE WERE NO OTHER ACFT PARKED THERE AT THE TIME. I WAS ALSO NOTIFIED THAT THE BARRIER WAS LESS THAN 1 FT TALL; AND MADE OF PVC. I ASSUME THE PVC WAS WHITE AND THAT IT BLENDS IN WITH THE CONCRETE BECAUSE WE NEVER SAW IT. THEY SAID THERE WERE LIGHTS ON IT; BUT I KNOW THEY WEREN'T ILLUMINATED BECAUSE WE DEFINITELY WOULD HAVE SEEN THEM. ANOTHER FACTOR WAS THE POOR AMBIENT LIGHT CONDITIONS BECAUSE THE SUN WAS JUST RISING AND WE WERE TAXIING INTO THE SUN. ACFT WAS INSPECTED UPON LNDG IN ZZZ AND NO DAMAGE WAS FOUND.