The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who�s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+252x^56+148x^57+342x^59+724x^60+3306x^62+1140x^63+192x^65+50x^66+198x^68+122x^69+78x^71+6x^74+2x^90

The gray image is a linear code over GF(3) with n=279, k=8 and d=168.
This code was found by Heurico 1.16 in 0.305 seconds.