The generator matrix

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

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 95.

Homogenous weight enumerator: w(x)=1x^0+486x^95+408x^96+2412x^98+1452x^99+5184x^101+3430x^102+9468x^104+5948x^105+15588x^107+8336x^108+20328x^110+10934x^111+22440x^113+11364x^114+19782x^116+9028x^117+13590x^119+5030x^120+6432x^122+2334x^123+2010x^125+576x^126+318x^128+146x^129+54x^131+34x^132+6x^134+18x^135+4x^138+2x^144+4x^147

The gray image is a linear code over GF(3) with n=168, k=11 and d=95.
This code was found by Heurico 1.16 in 410 seconds.