The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  X  1  1  X  1  X  1  X  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  X 2X 2X  X  X  X  0 2X  X 2X  X  0 2X  0  X  X  0 2X  X 2X 2X 2X  X  X  0 2X  0  0 2X  X  0 2X  X  0  X  X  0  X  0 2X  0  X  0 2X  X  X  0
 0  0  X  0  0  0  0  X 2X 2X 2X  0  0 2X  X 2X  X  0  X  X  0 2X  X  0 2X  X 2X  0  X  0 2X 2X 2X  X  0  X  X  0 2X  0  X 2X  X  X  0  0 2X  X  X  0  0  0  X  X  0  X  0
 0  0  0  X  0  0  X 2X  0 2X  0  0 2X  X  X 2X  0  X  0 2X  0 2X 2X  0 2X  0  X 2X 2X  X  X  X 2X  0 2X 2X  0  X 2X 2X  X 2X  X 2X  0 2X  0 2X 2X  X  X  0 2X  0  X  X  0
 0  0  0  0  X  0 2X 2X  X  0 2X 2X 2X  0 2X 2X  0 2X  X  0 2X 2X 2X  X  0  0 2X  X  0  X  0  X  0 2X 2X  0 2X  X  0 2X  X  0 2X  X 2X  0  X 2X 2X  0 2X  0 2X  X  X 2X 2X
 0  0  0  0  0  X 2X 2X 2X 2X 2X 2X  X 2X  X  X 2X  X 2X 2X 2X 2X  0 2X  0  X  0  0 2X  X 2X  0 2X  X  X  0  0  0  X  0  0  0  X  X  X  X  0  0  X 2X  0 2X 2X  0  X  0 2X

generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+48x^102+6x^103+130x^105+66x^106+128x^108+192x^109+106x^111+342x^112+54x^114+474x^115+56x^117+294x^118+50x^120+84x^121+38x^123+20x^126+34x^129+24x^132+20x^135+12x^138+4x^141+2x^147+2x^150

The gray image is a linear code over GF(3) with n=171, k=7 and d=102.
This code was found by Heurico 1.16 in 0.168 seconds.