The generator matrix

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

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+86x^42+172x^45+202x^48+162x^50+304x^51+972x^53+276x^54+1944x^56+268x^57+1296x^59+322x^60+256x^63+172x^66+98x^69+24x^72+6x^75

The gray image is a linear code over GF(3) with n=84, k=8 and d=42.
This code was found by Heurico 1.16 in 0.411 seconds.