The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X 2X  0  0
 0  0  X  0  0  0  0  0  0  0  X  X 2X 2X  0  X  X 2X 2X  0  X  X  0 2X  0 2X  0
 0  0  0  X  0  0  0  0  0  0 2X  X 2X  0  X 2X  0  X 2X 2X  0 2X  0  X 2X  0  0
 0  0  0  0  X  0  0  0  0  X 2X  0 2X  X 2X  X  0 2X  X  X 2X 2X  0  0  X  X  0
 0  0  0  0  0  X  0  0  0 2X 2X  0 2X  X  X 2X 2X  0  X 2X  X  0  X 2X 2X  0  0
 0  0  0  0  0  0  X  0  0 2X 2X  X  X  X 2X 2X  0  0 2X  0  X 2X 2X  X  X  0  0
 0  0  0  0  0  0  0  X  0 2X  0 2X 2X 2X 2X  X  X  0  0  X  X 2X  X  X 2X  X  0
 0  0  0  0  0  0  0  0  X 2X  0  X 2X  X  0 2X  X 2X  X  X 2X  X 2X 2X 2X  X  0

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+82x^33+276x^36+530x^39+964x^42+1322x^45+2208x^48+4374x^50+2628x^51+17496x^53+3084x^54+17496x^56+2946x^57+2546x^60+1554x^63+916x^66+416x^69+160x^72+42x^75+6x^78+2x^81

The gray image is a linear code over GF(3) with n=81, k=10 and d=33.
This code was found by Heurico 1.16 in 19.1 seconds.