The generator matrix

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

generates a code of length 28 over Z3[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+402x^53+420x^54+342x^56+554x^57+384x^59+72x^60+2x^63+6x^65+4x^66

The gray image is a linear code over GF(3) with n=252, k=7 and d=159.
This code was found by Heurico 1.16 in 4.09 seconds.