The generator matrix

 1  0  1  1  1  1  1  1 2X^2  1  1 2X^2+X  1 X^2+2X  1  1  1  X  1  0  1 X^2+2X  1  1  1 2X^2+X  1  1  1  1  0
 0  1  1  2 2X^2 2X^2+2  0 2X+1  1 X^2+1 2X^2+X  1 2X^2+1  1 2X X+1  X  1 2X^2+2X+2  1 2X^2+2X  1  2 2X^2+2X 2X^2+X+2  1 X^2+X X^2+2X+2  0 X^2+2X+2  1
 0  0 2X X^2 X^2+X 2X^2+X X^2+2X  X  X 2X^2+2X X^2+2X X^2+2X 2X^2  0 2X^2+2X X^2+2X 2X^2+X 2X^2+X  X 2X^2+2X 2X^2+X X^2+2X 2X  0 2X^2 X^2 X^2+X X^2+2X X^2 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+160x^57+330x^58+804x^59+588x^60+756x^61+1170x^62+846x^63+780x^64+768x^65+242x^66+48x^67+6x^68+16x^69+18x^70+8x^72+12x^73+6x^74+2x^78

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 0.0576 seconds.