We demonstrate a fast production of large Na-23 Bose-Einstein condensates in an optically plugged magnetic quadrupole trap. A single global minimum of the trapping potential is generated by slightly displacing the plug beam from the center of the quadrupole field. With a dark magneto-optical trap and a simple rf evaporation, our system produces a condensate with N approximate to 10(7) atoms every 17 s. The Majorana loss rates and the resultant heating rates for various temperatures are measured with and without plugging. The average energy of a spin-flipped atom is almost linearly proportional to temperature and determined to be about 60% of the average energy of a trapped atom. We present a numerical study of the evaporation dynamics in a plugged linear trap.