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

generates a code of length 71 over Z3[X]/(X^3) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+60x^139+270x^140+42x^141+54x^142+108x^143+20x^144+36x^145+108x^146+12x^147+12x^148+4x^150+2x^168

The gray image is a linear code over GF(3) with n=639, k=6 and d=417.
This code was found by Heurico 1.16 in 0.167 seconds.