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  0  0  0  0  0  0  0  0  X  X  X  X  X  X 2X  X 2X 2X 2X  X  0  0  0 2X  0
 0  0  X  0  0  0  0  0  X  X 2X 2X 2X  X 2X  X  0  0  X 2X 2X  0 2X  X  0 2X  0
 0  0  0  X  0  0  0  X 2X 2X 2X  X  X  0 2X  X 2X  0  X  X 2X  X 2X  X 2X  X  0
 0  0  0  0  X  0  0 2X 2X  X  X  0 2X 2X  0 2X  0 2X  X  0  X  X  0  0 2X 2X  X
 0  0  0  0  0  X  0 2X  X 2X  X 2X  0 2X  0  X 2X  0 2X  0  0  0  X  X 2X  0 2X
 0  0  0  0  0  0  X  X  0  X  0  X  0 2X 2X  X  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X

generates a code of length 27 over Z3[X]/(X^2) 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+324x^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=81, k=8 and d=39.
This code was found by Heurico 1.16 in 0.332 seconds.