The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+342x^60+294x^63+72x^66+18x^69+2x^81

The gray image is a linear code over GF(3) with n=279, k=6 and d=180.
This code was found by Heurico 1.16 in 6.67 seconds.