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

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+52x^96+158x^99+208x^102+18x^104+204x^105+180x^107+240x^108+720x^110+192x^111+1440x^113+200x^114+1440x^116+164x^117+576x^119+182x^120+160x^123+168x^126+104x^129+74x^132+52x^135+14x^138+12x^141+2x^156

The gray image is a linear code over GF(3) with n=171, k=8 and d=96.
This code was found by Heurico 1.16 in 1.05 seconds.