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

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+114x^139+162x^140+44x^141+324x^143+22x^144+42x^148+8x^150+4x^153+6x^157+2x^159

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 5.01 seconds.