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.