The generator matrix

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

generates a code of length 42 over Z3[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+96x^79+156x^80+32x^81+78x^82+48x^83+20x^84+60x^85+20x^87+42x^88+108x^89+30x^91+6x^92+12x^94+4x^96+6x^97+6x^98+4x^102

The gray image is a linear code over GF(3) with n=126, k=6 and d=79.
This code was found by Heurico 1.16 in 1.31 seconds.