The generator matrix

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

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+370x^51+216x^52+1432x^54+864x^55+2230x^57+864x^58+544x^60+30x^63+2x^66+2x^69+4x^72+2x^78

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 0.0519 seconds.