The generator matrix

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

generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+116x^42+30x^43+210x^44+374x^45+306x^46+1038x^47+1100x^48+756x^49+2484x^50+2518x^51+2352x^52+5322x^53+4486x^54+3402x^55+7410x^56+5274x^57+3726x^58+5994x^59+3880x^60+2100x^61+3108x^62+1502x^63+450x^64+678x^65+312x^66+74x^69+36x^72+10x^75

The gray image is a linear code over GF(3) with n=84, k=10 and d=42.
This code was found by Heurico 1.16 in 14 seconds.