The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1
0 X 0 0 0 0 X 2X 2X 0 0 X X X X X X 0 X 2X X X 0 0 X 0 2X 2X
0 0 X 0 0 X 2X 0 2X 0 X X 2X 2X 0 X 0 X 2X 2X 0 2X X 2X X 0 X 2X
0 0 0 X 0 2X 2X X 0 X X 0 0 X 2X X X 0 2X X X X X 0 0 2X 0 X
0 0 0 0 X 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 0 2X 0 0 X 2X X 0 X X X 2X
generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 51.
Homogenous weight enumerator: w(x)=1x^0+90x^51+240x^54+324x^57+36x^60+36x^69+2x^81
The gray image is a linear code over GF(3) with n=84, k=6 and d=51.
This code was found by Heurico 1.16 in 0.667 seconds.