The generator matrix

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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+210x^52+348x^53+206x^54+510x^55+954x^56+588x^57+2472x^58+1914x^59+3482x^60+4632x^61+1932x^62+684x^63+660x^64+414x^65+96x^66+246x^67+246x^68+44x^69+18x^70+24x^71+2x^78

The gray image is a linear code over GF(3) with n=270, k=9 and d=156.
This code was found by Heurico 1.16 in 8.94 seconds.