A B727 CREW INSTRUCTED TO TURN OFF RWY ONTO A TXWY THAT HAS A POORLY MARKED DITCH.

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LANDED AT MGA AT APPROX XA00 ON RWY 9. DID A 180 DEG TURN TO TAXI BACK TO THE TERMINAL. THERE WAS ANOTHER ACFT ON FINAL. TWR TOLD US TO TAKE THE FIRST TXWY ON THE R AND THE FO REPEATED 'ROGER; UNDERSTAND TURN R ON THE FIRST TXWY;' WHICH WE DID. WE TAXIED TOWARD THE TERMINAL ONLY TO DISCOVER THAT THERE WAS A DITCH CUT ACROSS THE TXWY WITH 1 CONE ON THE TAXI LINE. TWR THEN TOLD US THAT THE TXWY WAS CLOSED AND THAT WE HAD TO TURN AROUND AND TAXI BACK TO THE RWY. WE TOLD HIM THAT WE WERE UNABLE DUE TO THE TXWY BEING TOO NARROW. THE CLOSURE WAS NOT IN THE NOTAMS AND THERE WERE NO CONES AT THE ENTRANCE OF THE TXWY. FURTHER; THE FO AND I AGREE THAT TWR MUST HAVE FORGOTTEN ABOUT THE CONSTRUCTION BECAUSE WE BOTH HEARD HIM SAY 'TAKE THE FIRST TXWY.' WE SUBSEQUENTLY TALKED TO THE CTLR WHO SAYS THAT HE SAID THE SECOND TXWY. REGARDLESS; THE FO DID READ BACK THE FIRST TXWY. NET RESULT WAS ABOUT A 20 MIN DELAY WHILE WE WERE TUGGED TO THE GATE. THE COMPANY OPS MGR SHOULD HAVE RPTED THE CLOSURE FOR INCLUSION IN THE NOTAMS. IN ADDITION; THERE WERE NO FLASHING LIGHTS; ETC; TO INDICATE CONSTRUCTION. IN FACT; IF IT WEREN'T FOR THE CONE; WE COULD HAVE ENDED UP POSSIBLY IN THE DITCH. WE TRIED REPEATEDLY TO GET OPS ON THE OPS FREQ BUT NO ONE WOULD ANSWER. THE TAXI LIGHTS WERE ON FOR THE FIRST TXWY WHICH WAS ALSO MISLEADING. SOMEONE NEEDS TO LOOK CLOSELY AT OPS AT MGA.