The generator matrix

 1  0  1  1  1  1  1  0  1  0  1  1  1  1  0  1  1  1  0  X  1  X  1  1 2X  X  1
 0  1  1  2  0  1  2  1 2X+1  1  0  2  0 X+1  1  2 2X+1  X  1  1 2X+1  1  0  X  1  X  0
 0  0 2X  0  0  0  0  0  0  0 2X 2X 2X  X 2X  X  X 2X  X  X 2X  0  X  X  0  0  0
 0  0  0  X  0  0  0  X 2X  X  X  0 2X 2X  0  X  X  X  X 2X  X  X 2X  0  0  X  0
 0  0  0  0  X  0  X  X  X  X 2X 2X  0  X  0  X  X  X  0  X  X 2X  X 2X  X 2X  0
 0  0  0  0  0 2X 2X  0 2X  X 2X  0  X  X 2X 2X  0 2X 2X 2X  X  X 2X  X  X 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+66x^42+6x^44+224x^45+96x^46+60x^47+444x^48+132x^49+240x^50+642x^51+402x^52+480x^53+736x^54+444x^55+480x^56+894x^57+300x^58+192x^59+432x^60+84x^61+146x^63+30x^66+12x^69+18x^72

The gray image is a linear code over GF(3) with n=81, k=8 and d=42.
This code was found by Heurico 1.16 in 0.214 seconds.