The generator matrix

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

generates a code of length 26 over Z3[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+594x^44+794x^45+1872x^46+4464x^47+8152x^48+8514x^49+20136x^50+23904x^51+27108x^52+33864x^53+25510x^54+11898x^55+7596x^56+2032x^57+180x^58+348x^59+108x^60+66x^62+2x^63+4x^66

The gray image is a linear code over GF(3) with n=234, k=11 and d=132.
This code was found by Heurico 1.16 in 21.6 seconds.