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

generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+78x^96+126x^97+126x^98+110x^99+264x^100+342x^101+104x^102+420x^103+456x^104+90x^105+468x^106+600x^107+68x^108+624x^109+636x^110+54x^111+528x^112+462x^113+58x^114+378x^115+246x^116+44x^117+84x^118+48x^119+42x^120+24x^121+34x^123+12x^126+16x^129+10x^132+8x^135

The gray image is a linear code over GF(3) with n=162, k=8 and d=96.
This code was found by Heurico 1.16 in 0.594 seconds.