The generator matrix

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

generates a code of length 72 over Z3[X]/(X^2) who´s minimum homogenous weight is 134.

Homogenous weight enumerator: w(x)=1x^0+294x^134+256x^135+762x^137+420x^138+792x^140+324x^141+726x^143+362x^144+522x^146+276x^147+492x^149+234x^150+318x^152+128x^153+246x^155+96x^156+150x^158+72x^159+48x^161+18x^162+18x^164+6x^167

The gray image is a linear code over GF(3) with n=216, k=8 and d=134.
This code was found by Heurico 1.16 in 0.699 seconds.