The generator matrix

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

generates a code of length 26 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+42x^45+18x^46+64x^48+108x^49+48x^51+216x^52+24x^54+144x^55+20x^57+16x^60+14x^63+6x^66+8x^69

The gray image is a linear code over GF(3) with n=78, k=6 and d=45.
This code was found by Heurico 1.16 in 0.00676 seconds.