The generator matrix

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

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+46x^51+42x^52+78x^53+356x^54+60x^55+1008x^56+378x^57+36x^58+18x^59+68x^60+12x^61+30x^62+34x^63+12x^64+6x^66+2x^81

The gray image is a linear code over GF(3) with n=252, k=7 and d=153.
This code was found by Heurico 1.16 in 0.0143 seconds.