#Python 2, 127 bytes

lambda s:''.join("IVMB  T  K 9LZF 1HWO3 GUS4 8 7A  E QR 26   NJX    Y0P 5D  C"[(int('0'+l)^2162146)%59]for l in s.split('000'))

Try it online!

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.

Python 2, 127 bytes

lambda s:''.join("IVMB  T  K 9LZF 1HWO3 GUS4 8 7A  E QR 26   NJX    Y0P 5D  C"[(int('0'+l)^2162146)%59]for l in s.split('000'))

Try it online!

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.

Python 2, 125 bytes

lambda s:''.join(" NTJ  M I 8WD Q KLYC7UB VP H2059  A  E  S  4X   GO61 R3ZF"[(int('0'+l)^1922988)%57]for l in s.split('000'))

Try it online!

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.

#Python 2, 127 bytes

lambda s:''.join("IVMB  T  K 9LZF 1HWO3 GUS4 8 7A  E QR 26   NJX    Y0P 5D  C"[(int('0'+l)^2162146)%59]for l in s.split('000'))

Try it online!

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.

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'))

Try it online!

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.

Python 2, 125 bytes

lambda s:''.join(" NTJ  M I 8WD Q KLYC7UB VP H2059  A  E  S  4X   GO61 R3ZF"[(int('0'+l)^1922988)%57]for l in s.split('000'))

Try it online!

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.