The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+890x^57+900x^58+1254x^59+3868x^60+1332x^61+2376x^62+3974x^63+1416x^64+1212x^65+2014x^66+384x^67+12x^68+14x^69+6x^70+6x^71+12x^72+12x^73

The gray image is a linear code over GF(3) with n=279, k=9 and d=171.
This code was found by Heurico 1.16 in 0.39 seconds.