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.