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.