The generator matrix

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

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+60x^42+246x^44+314x^45+1038x^47+730x^48+2082x^50+1272x^51+3480x^53+1672x^54+3822x^56+1444x^57+1914x^59+810x^60+540x^62+194x^63+40x^66+18x^69+6x^72

The gray image is a linear code over GF(3) with n=81, k=9 and d=42.
This code was found by Heurico 1.16 in 1.74 seconds.