The generator matrix

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

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+492x^139+810x^140+320x^141+1116x^142+702x^143+318x^144+690x^145+522x^146+180x^147+558x^148+522x^149+58x^150+198x^151+36x^152+2x^153+6x^154+6x^156+6x^157+2x^159+6x^163+6x^166+4x^168

The gray image is a linear code over GF(3) with n=648, k=8 and d=417.
This code was found by Heurico 1.16 in 0.265 seconds.