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

generates a code of length 70 over Z3[X]/(X^3) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+114x^137+188x^138+360x^141+4x^144+42x^146+8x^147+4x^153+6x^155+2x^156

The gray image is a linear code over GF(3) with n=630, k=6 and d=411.
This code was found by Heurico 1.16 in 4.21 seconds.