The generator matrix

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

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+336x^57+534x^58+680x^60+1644x^61+1212x^63+1620x^64+418x^66+60x^67+22x^69+30x^70+2x^72+2x^84

The gray image is a linear code over GF(3) with n=279, k=8 and d=171.
This code was found by Heurico 1.16 in 1.16 seconds.