The MD-11 was flying an approach to runway 11 at Buenos Aires/Ezeiza, Argentina when the pilot decided to go around due to vibrations and a nose down tendency of the airplane. The same issues occurred during the second approach. The airplane overflew the runway threshold at 70-100 m altitude and touched down at 1200-1500 m on a wet runway. The airplane failed to stop on the runway and ran onto the grass at a speed of 60 knots. It came to rest after 50 m. Probable Cause: Departed the runway on the opposite side from that used for landing causing minor damage to the aircraft and the ILS localizer antenna for that runway, due to an excessively long touch down on the wet runway with wrong markings on the airspeed indicators. Contributing factors: Failure during maintenance and repair of the radome that caused the clogged pitot tubes drains. Unfavorable weather conditions.