The generator matrix

 1  0  0  1  1  1  1  1  1 2X  1  1  X  1 2X  1  1  1  1  0  X  X  1  1  1  1  1  1
 0  1  0 2X  1 2X+1  2  0 X+2  1 2X+2 2X  1 2X+1  1 X+1 X+2 2X  0  1  1 2X  1 X+1  1  2 2X+1 2X+1
 0  0  1 2X+1  1 2X 2X+2  2  X  1 X+2 X+1  X X+2 X+2  1  0 2X 2X+2 2X+1 X+2  1  2  X X+1  2 2X+2  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+74x^51+48x^52+54x^53+132x^54+66x^55+90x^56+84x^57+12x^58+64x^60+24x^61+50x^63+6x^64+18x^65+6x^67

The gray image is a linear code over GF(3) with n=84, k=6 and d=51.
This code was found by Heurico 1.13 in 0.0573 seconds.