The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+38x^39+144x^42+214x^45+260x^48+486x^50+230x^51+1944x^53+13446x^54+1944x^56+348x^57+284x^60+184x^63+106x^66+44x^69+6x^72+4x^75

The gray image is a linear code over GF(3) with n=243, k=9 and d=117.
This code was found by Heurico 1.16 in 0.917 seconds.