The generator matrix

 1  0  0  0  1  1  1  1  1  1 2X^2+X  1  X  1 X^2  1 X^2+2X  1  1  1 X^2+X 2X^2 X^2+X  1  1  1
 0  1  0  0 2X^2+2X 2X^2+1 X^2 2X^2+X 2X+1 2X^2+X+2  1  X  1 X^2+X+1  1 2X^2+X+1  1 2X^2+2 X^2+X+2 2X^2+X+2 X^2+X  1 X^2 2X^2+2X 2X+1  0
 0  0  1  0 2X^2+2X+1 2X^2+1 X^2+2X+1 2X^2+2X+2  2 X^2+X X^2+2X+1 X^2 2X^2+2 X+2 X^2+2X+2  X  X  0 2X^2+X+2 2X^2+2  1  2  1 2X X^2+X 2X
 0  0  0  1 2X^2+2X+2 2X^2+X  1 2X^2 X+2 2X+1 2X^2+X+2 X^2+2X+2 2X^2+X+1 2X^2+2X+1 2X^2+2X 2X  1 2X^2+X+2 2X^2+1 2X^2+2X 2X^2+1 X^2+2X+2 2X^2 X+1  1 X^2+2X

generates a code of length 26 over Z3[X]/(X^3) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+312x^43+960x^44+3592x^45+5742x^46+10740x^47+26462x^48+27996x^49+54312x^50+80642x^51+76146x^52+95310x^53+82434x^54+37638x^55+18294x^56+9180x^57+1326x^58+174x^59+94x^60+42x^61+30x^62+10x^63+4x^66

The gray image is a linear code over GF(3) with n=234, k=12 and d=129.
This code was found by Heurico 1.16 in 171 seconds.