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.