The generator matrix

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

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+86x^51+48x^52+108x^53+118x^54+36x^55+90x^57+54x^58+56x^60+24x^61+54x^62+50x^63+2x^69+2x^72

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 0.00543 seconds.