Python 2, 128 bytes
lambda s:''.join(" 2A V ZYRS9 8W5CP E ULM JGX H D Q T6 1K 4 7 I 3FB0 N O"[(int('0'+l)^132270)%61]for l in s.split('000'))
Building off of TFeld's solution by removing replace and by working in base 10, at the cost of a bitwise xor and a longer reference string.
