The generator matrix

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

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 134.

Homogenous weight enumerator: w(x)=1x^0+450x^134+680x^135+828x^136+1656x^137+1862x^138+2718x^139+3216x^140+3444x^141+6318x^142+5028x^143+4480x^144+8010x^145+4908x^146+4142x^147+4464x^148+2478x^149+1692x^150+972x^151+840x^152+256x^153+18x^154+180x^155+116x^156+126x^158+66x^159+54x^161+28x^162+6x^164+12x^167

The gray image is a linear code over GF(3) with n=648, k=10 and d=402.
This code was found by Heurico 1.16 in 12.8 seconds.