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.