The generator matrix

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

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+124x^42+198x^43+618x^44+1094x^45+1398x^46+2424x^47+3364x^48+3762x^49+6570x^50+7840x^51+8100x^52+12960x^53+13338x^54+14136x^55+18204x^56+15772x^57+14538x^58+15834x^59+11748x^60+7842x^61+7158x^62+4714x^63+2178x^64+1674x^65+970x^66+330x^67+168x^68+68x^69+6x^70+14x^72+2x^78

The gray image is a linear code over GF(3) with n=84, k=11 and d=42.
This code was found by Heurico 1.16 in 149 seconds.