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

generates a code of length 71 over Z3[X]/(X^3) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+88x^138+72x^140+156x^141+1620x^142+72x^143+98x^144+18x^146+56x^147+4x^150+2x^213

The gray image is a linear code over GF(3) with n=639, k=7 and d=414.
This code was found by Heurico 1.16 in 0.197 seconds.