The generator matrix

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

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+134x^102+18x^103+66x^104+374x^105+192x^106+132x^107+526x^108+186x^109+210x^110+488x^111+216x^112+366x^113+654x^114+372x^115+342x^116+538x^117+240x^118+222x^119+520x^120+198x^121+108x^122+218x^123+30x^124+12x^125+104x^126+6x^127+22x^129+24x^132+24x^135+4x^138+8x^141+4x^144+2x^147

The gray image is a linear code over GF(3) with n=171, k=8 and d=102.
This code was found by Heurico 1.16 in 0.676 seconds.