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

generates a code of length 71 over Z3[X]/(X^3) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+144x^135+144x^138+486x^140+164x^141+972x^143+76x^144+92x^147+50x^150+32x^153+10x^156+6x^162+6x^165+2x^171+2x^177

The gray image is a linear code over GF(3) with n=639, k=7 and d=405.
This code was found by Heurico 1.16 in 0.201 seconds.