The generator matrix

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

generates a code of length 26 over Z3[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+142x^42+186x^44+198x^45+648x^46+492x^47+3194x^48+3888x^49+4056x^50+12224x^51+7776x^52+7320x^53+12148x^54+5184x^55+912x^56+302x^57+156x^59+158x^60+44x^63+14x^66+4x^69+2x^72

The gray image is a linear code over GF(3) with n=234, k=10 and d=126.
This code was found by Heurico 1.16 in 3.8 seconds.