The generator matrix

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

generates a code of length 28 over Z3[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+122x^51+312x^52+660x^53+868x^54+564x^55+1128x^56+1262x^57+684x^58+630x^59+236x^60+30x^61+6x^62+10x^63+12x^64+6x^65+10x^66+18x^67+2x^69

The gray image is a linear code over GF(3) with n=252, k=8 and d=153.
This code was found by Heurico 1.16 in 0.051 seconds.