The generator matrix

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

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+432x^59+350x^60+432x^62+482x^63+432x^65+48x^66+4x^69+6x^72

The gray image is a linear code over GF(3) with n=279, k=7 and d=177.
This code was found by Heurico 1.16 in 84 seconds.