A BE76 ON ROLLOUT AT GREATER THAN 55 KTS HAD THE NOSE LANDING GEAR HANDLE INADVERTENTLY MOVED TO RETRACT. NOSE GEAR RETRACTED; INCURRING DAMAGE TO PROPS AND ENGS.

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AFTER FLYING THE ILS RWY 28R INTO ZZZ; MY INSTRUCTOR AND I WERE MAKING A CIRCLE-TO-LAND FOR RWY 10L. WE WERE EXECUTING A SHORT FIELD LNDG TO A FULL STOP. ON DOWNWIND; BASE; AND FINAL; WE BOTH VERIFIED THE GEAR WAS DOWN AND LOCKED (3 GREEN). AFTER TOUCHING DOWN; I INADVERTENTLY RETRACTED THE LNDG GEAR; INSTEAD OF THE FLAPS. IMMEDIATELY (LITERALLY LESS THAN 1 SECOND) AFTER RETRACTING THE GEAR; MY INSTRUCTOR AND I BOTH REACHED OVER TO THE GEAR HANDLE AND PUT IT BACK DOWN; BUT THE NOSE GEAR HAD ALREADY RETRACTED/COLLAPSED; AND THE PLANE SLID TO A STOP ON THE RWY. THE MAIN GEAR DID NOT RETRACT. I BELIEVE THE MAIN FACTORS LEADING UP TO THIS INCIDENT WERE BEECHCRAFT'S FAILURE TO DESIGN A SYS WHICH DISABLES GEAR RETRACTION WHILE ON THE GND. THE AIR PRESSURE SWITCH MAKES IT POSSIBLE TO RETRACT THE GEAR WHILE THE AIRPLANE IS STILL ON THE GND -- A POOR SYS DESIGN; ESPECIALLY SINCE ROTATION SPD IS 71 KTS. IN ADDITION; THE GEAR HANDLE UTILIZES THE SAME PULL LIFT MOVEMENT AS THE FLAPS HANDLE. THIS IS NO EXCUSE FOR WHAT HAPPENED; HOWEVER; I FEEL THAT IF THE DESIGN WERE A LITTLE DIFFERENT THIS COULD HAVE BEEN AVOIDED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR SAID THE GND SENSING WAS EXPLAINED BRIEFLY AND THE CRITICAL AIRSPD WAS 55 KTS AND HE EXCEEDED THIS SPD ON ROLLOUT. BUT THE WRONG HANDLE WAS ACTIVATED AND THE NOSE GEAR RETRACTED IMMEDIATELY DAMAGING THE PROPS AND ENGS AND SLIGHT SKIN DAMAGE. THIS IS THE FIRST AIRPLANE FLOWN WITH THIS KIND OF GND SENSING AND THE RPTR BELIEVES THIS WAS A FACTOR IN THIS INCIDENT.