The generator matrix

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

generates a code of length 28 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+8x^54+210x^56+18x^57+6x^65

The gray image is a linear code over GF(3) with n=252, k=5 and d=162.
This code was found by Heurico 1.16 in 0.00401 seconds.