The generator matrix

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

generates a code of length 26 over Z3[X]/(X^2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+82x^42+18x^44+112x^45+144x^47+98x^48+432x^50+112x^51+576x^53+86x^54+288x^56+92x^57+70x^60+42x^63+26x^66+6x^69+2x^72

The gray image is a linear code over GF(3) with n=78, k=7 and d=42.
This code was found by Heurico 1.16 in 0.0433 seconds.