The generator matrix

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

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+324x^134+266x^135+846x^137+582x^138+252x^139+1470x^140+1056x^141+864x^142+3000x^143+2736x^144+1404x^145+3096x^146+1376x^147+396x^148+684x^149+180x^150+360x^152+210x^153+204x^155+92x^156+168x^158+60x^159+42x^161+12x^164+2x^192

The gray image is a linear code over GF(3) with n=648, k=9 and d=402.
This code was found by Heurico 1.16 in 3.19 seconds.