The generator matrix

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

generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+204x^52+140x^54+66x^55+60x^57+90x^58+18x^60+102x^61+12x^63+24x^64+12x^66

The gray image is a linear code over GF(3) with n=84, k=6 and d=52.
This code was found by Heurico 1.16 in 6.67 seconds.