The generator matrix

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

generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+54x^96+18x^98+230x^99+42x^100+114x^101+422x^102+156x^103+216x^104+792x^105+270x^106+414x^107+1290x^108+552x^109+666x^110+1678x^111+912x^112+864x^113+1864x^114+972x^115+846x^116+1898x^117+894x^118+648x^119+1328x^120+444x^121+378x^122+828x^123+108x^124+180x^125+266x^126+24x^127+30x^128+120x^129+72x^132+60x^135+16x^138+8x^141+8x^144

The gray image is a linear code over GF(3) with n=171, k=9 and d=96.
This code was found by Heurico 1.16 in 5.76 seconds.