The generator matrix

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

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+180x^55+306x^56+758x^57+552x^58+768x^59+1342x^60+750x^61+828x^62+710x^63+288x^64+18x^65+10x^66+6x^67+6x^68+12x^69+6x^70+18x^71+2x^78

The gray image is a linear code over GF(3) with n=270, k=8 and d=165.
This code was found by Heurico 1.16 in 0.0547 seconds.