The generator matrix

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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+526x^54+396x^55+810x^56+1552x^57+1728x^58+3240x^59+2404x^60+3132x^61+3240x^62+1686x^63+576x^64+248x^66+134x^69+10x^72

The gray image is a linear code over GF(3) with n=270, k=9 and d=162.
This code was found by Heurico 1.16 in 15 seconds.