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 X 1
0 X 0 0 0 0 0 0 0 0 X X X X X 2X 2X 2X 0 2X 2X X X X X 0
0 0 X 0 0 0 0 0 X X 2X 2X 2X X 2X 0 2X 2X X 0 2X 0 2X X 2X X
0 0 0 X 0 0 0 X 2X 2X 2X X X 0 0 X 0 0 X 0 2X X X 2X 2X 0
0 0 0 0 X 0 0 2X 2X X X 0 2X 2X 2X X 0 0 0 X 2X X X X 0 X
0 0 0 0 0 X 0 2X X 2X X 2X 0 2X 2X 0 0 X X 2X X X 2X 0 X 2X
0 0 0 0 0 0 X X 0 X 0 X 0 2X 0 2X 2X 0 2X X 0 X 2X X 2X 0
generates a code of length 26 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.
Homogenous weight enumerator: w(x)=1x^0+106x^39+204x^42+254x^45+274x^48+1458x^50+282x^51+2916x^53+290x^54+324x^57+264x^60+126x^63+50x^66+6x^69+4x^72+2x^75
The gray image is a linear code over GF(3) with n=78, k=8 and d=39.
This code was found by Heurico 1.16 in 0.373 seconds.