The generator matrix

 1  0  0  0  0  1  1  1  1  1  X  1  1  1  1  X  1  1 2X  1  1  1  X  1  0 2X  1
 0  1  0  0  0 2X  1 X+1 2X+2  2  1  X X+2 2X+2 2X  1 X+2  1  1  1 2X+1 X+1  0 2X+1  1  1  0
 0  0  1  0  0  0  0 2X 2X 2X 2X  1  2 X+2 2X+2  1 2X+1 2X+2  2  1  1  2  1 X+2 2X+2  X  X
 0  0  0  1  0 2X+1  1 2X+2 2X X+2 2X+2 2X+1  2  X  0 X+1 2X X+1  0 2X X+2  0 2X+2 X+2 2X+1  2 2X
 0  0  0  0  1 2X+2  X 2X+1  1 X+2  2  1 X+1  X X+1 2X+1  0  2 X+1 X+2  X  0  1 2X+1  X  X  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+248x^42+84x^43+330x^44+1462x^45+894x^46+1050x^47+3154x^48+1620x^49+2022x^50+6264x^51+3144x^52+3546x^53+9176x^54+3546x^55+3516x^56+8040x^57+2784x^58+2064x^59+3564x^60+912x^61+534x^62+810x^63+132x^64+60x^65+72x^66+6x^67+4x^69+8x^72+2x^75

The gray image is a linear code over GF(3) with n=81, k=10 and d=42.
This code was found by Heurico 1.16 in 17.9 seconds.