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

generates a code of length 42 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+82x^78+58x^81+162x^82+324x^85+58x^87+8x^90+20x^96+14x^99+2x^123

The gray image is a linear code over GF(3) with n=126, k=6 and d=78.
This code was found by Heurico 1.16 in 0.0166 seconds.