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.