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^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2  0 2X^2 2X^2 X^2 X^2 X^2 X^2  0
 0  0 X^2  0  0  0  0  0 X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2  0 2X^2 2X^2 X^2  0 2X^2  0 2X^2 X^2 2X^2 X^2
 0  0  0 X^2  0  0  0 X^2 2X^2 2X^2 2X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 2X^2 X^2 X^2 2X^2 2X^2  0
 0  0  0  0 X^2  0  0 2X^2 2X^2 X^2 X^2  0 2X^2 2X^2 2X^2 X^2  0  0  0 X^2 2X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0 2X^2 X^2 2X^2 X^2 2X^2  0 2X^2 2X^2  0  0 X^2 X^2 2X^2 X^2 X^2 2X^2  0 X^2 2X^2
 0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 2X^2  0 2X^2 2X^2  0 2X^2 X^2  0 X^2 2X^2 X^2 2X^2  0

generates a code of length 26 over Z3[X]/(X^3) 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+13122x^52+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=234, k=9 and d=117.
This code was found by Heurico 1.16 in 0.976 seconds.