The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+108x^59+198x^60+348x^63+18x^66+54x^68+2x^81

The gray image is a linear code over GF(3) with n=279, k=6 and d=177.
This code was found by Heurico 1.16 in 0.403 seconds.