The generator matrix

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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+708x^55+1164x^56+1302x^57+3000x^58+2658x^59+1856x^60+3360x^61+2280x^62+1280x^63+1488x^64+528x^65+6x^66+24x^67+6x^68+10x^69+6x^70+6x^71

The gray image is a linear code over GF(3) with n=270, k=9 and d=165.
This code was found by Heurico 1.16 in 0.343 seconds.