INSTRUCTOR WITH SPI TAXIES INTO PARKED VEHICLE AND OVER BARRICADES.

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MY STUDENT AND I JUST LANDED ON RWY 19R. WE WERE INSTRUCTED BY THE TWR TO TAXI ONTO ALPHA 2 AND CONTACT GND. WE CONTACTED GND AND RECEIVED CLRNC TO TAXI TO TRANSIENT RAMP. WE STARTED TO TAXI AND ROUNDED THE CORNER FROM ALPHA 2; TURNING SBOUND ON ALPHA. DURING TRANSITION FROM THE TURN TO A SBOUND HDG ON ALPHA MY STUDENT WAS ROLLING TOWARD THE TAXIWAY CTRLINE BUT NOT QUITE ON IT YET. WE WERE MAYBE A FT OR 2 L OF CTR AS WE TURNED SBOUND. ON THE CORNER OF THE MAIN RAMP; WHERE THE CONSTRUCTION IS PRESENTLY TAKING PLACE; WAS A ROLLER MACHINE POSITIONED ON THE TAXIWAY APPROX 1 OR 2 FT W OF THE BARRICADE. AT THIS TIME; I NOTICED THAT THE R WING OF THE ACFT WAS GOING TO PASS THE ROLLER MACHINE VERY CLOSELY. IMMEDIATELY; I TOLD SPI TO TAXI TOWARD THE E SIDE OF THE TAXIWAY AWAY FROM THE ROLLER MACHINE AND MY L FT MOVED ONTO THE L BRAKE/RUDDER PEDAL TO HELP HIM ACCOMPLISH THIS. BUT; I COULD NOT ACT FAST ENOUGH TO PREVENT THE WING FROM STRIKING THE ROLLER MACHINE. AS THE R WING STRUCK; WE PIVOTED R AND OVER THE BARRICADE. WE THEN STOPPED THE PLANE AS SOON AS WE STOPPED SHAKING FROM GOING OVER THE BARRICADE. WE THEN SHUT DOWN THE PLANE AND LEFT IT IN ITS EXACT POS. I ATTEMPTED TO FIND MY FLT COMMANDER AND COULD NOT FIND HIM. I THEN LOOKED FOR ANY OTHER FLT COMMANDER AND COULD NOT LOCATE THEM. NEXT; I WENT TO THE SHOP AND FOUND OUR CHIEF MECH; AND TOOK HIM TO EXAMINE THE ACFT.