The generator matrix

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

generates a code of length 28 over Z3[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+66x^56+4x^57+6x^59+2x^63+2x^66

The gray image is a linear code over GF(3) with n=252, k=4 and d=168.
This code was found by Heurico 1.16 in 0.0042 seconds.