The generator matrix

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

generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+228x^50+156x^51+390x^53+230x^54+282x^56+130x^57+312x^59+130x^60+204x^62+64x^63+42x^65+14x^66+2x^69+2x^72

The gray image is a linear code over GF(3) with n=84, k=7 and d=50.
This code was found by Heurico 1.13 in 0.0146 seconds.