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
 0  X  0  0  0  0  X 2X 2X  0  0  X  X  X  X  X  X  X  0 2X  0 2X  0 2X  0  X 2X  X 2X 2X  0  0 2X  X  0  X  X  X  X  0  0  0  X  0  X  0  0  X  X 2X 2X 2X 2X  X  0  X  0  X 2X 2X 2X  0 2X 2X  0  X  0  X
 0  0  X  0  0  X 2X  0 2X  0  X  X 2X 2X  0  X  0  X  X  X  X  0  0 2X 2X  X  X 2X  0 2X  0  X  X  0 2X 2X  0  X  0 2X 2X 2X  X 2X 2X  0  0 2X  X  0  0  0  X  X  X 2X  0  X  0  X  X 2X  X  0  X  0 2X 2X
 0  0  0  X  0 2X 2X  X  0  X  X  0  0  X 2X  X  X 2X 2X  0  0 2X 2X 2X 2X 2X  X  X  0  X 2X  X 2X 2X  X 2X  X  0  0  0  X  0  X 2X  0  0  X  X  0 2X 2X  0  0 2X 2X  0 2X  X  0  X  0  0 2X  X  0 2X 2X 2X
 0  0  0  0  X 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  X  0  0 2X 2X  X 2X  X 2X  0 2X  0  0 2X 2X  X  0  0  0 2X  0  X  X 2X 2X  X  0  X 2X  X  X  X  0  X 2X  X  0  X 2X  0  0  X 2X 2X  0 2X  X  X  X 2X  X

generates a code of length 68 over Z3[X]/(X^2) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+22x^129+58x^132+64x^135+486x^136+48x^138+24x^141+16x^144+2x^147+6x^150+2x^204

The gray image is a linear code over GF(3) with n=204, k=6 and d=129.
This code was found by Heurico 1.16 in 0.067 seconds.