The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 0 2 1 X X+2 2X+1 1 2X+1 1 2 0 2X+1 0 2 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X X X 2X X X X 2X 2X 2X 0 X X
0 0 0 X 0 0 0 0 X 2X X 2X X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X X
0 0 0 0 X 0 0 X 2X 2X X X 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 X 0 0 0 0
0 0 0 0 0 2X 0 2X X 0 X X 2X 2X X 2X 0 X 0 2X X 0 0 X 0 2X 2X 2X
0 0 0 0 0 0 X 2X 0 2X 2X X X 2X 2X X 2X X 0 0 X 2X X 0 0 2X 0 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+70x^42+18x^43+6x^44+232x^45+84x^46+72x^47+602x^48+252x^49+360x^50+1402x^51+738x^52+960x^53+2448x^54+1290x^55+1440x^56+3008x^57+1152x^58+1152x^59+2094x^60+648x^61+384x^62+784x^63+192x^64+164x^66+104x^69+18x^72+6x^75+2x^78
The gray image is a linear code over GF(3) with n=84, k=9 and d=42.
This code was found by Heurico 1.16 in 2.01 seconds.