The generator matrix

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

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+32x^42+110x^45+92x^48+162x^50+86x^51+648x^53+104x^54+648x^56+94x^57+80x^60+72x^63+28x^66+18x^69+10x^72+2x^75

The gray image is a linear code over GF(3) with n=81, k=7 and d=42.
This code was found by Heurico 1.16 in 0.0429 seconds.