What was found
SFO - FLT 0020 - AFTER TAKEOFF SFO, 5 KNOTS PRIOR TO V1, AIRPLANE VIBRATED EXCESSIVELY. AFTER GEAR RETRACTION, ALL THREE RED LIGHTS STAYED ILLUMINATED. GEAR HANDLE POPPED OUT AND THEN BACK INTO THE UP DEFAULT. VISUAL INSPECTION SHOWED RIGHT MAIN GEAR DOORS OPEN SLIGHTLY. ALTERNATE GEAR EXTENSION WAS PERFORMED WITH SUBSEQUENT INSPECTION OF THE TIRES. NR 4 MAIN TIRE WAS FOUND SHREDDED. RETURNED AND LANDED SFO WITHOUT INCIDENT. REPLACED NR 4 MLG TIRE PER MM. STRAIGHTENED FOLLOW-UP DOOR SEAL. PERFORMED GEAR SWING SEVERAL TIMES. SYSTEM GROUND CHECKED, NORMAL OPERATION. (X)