The generator matrix

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

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+228x^52+438x^53+890x^54+1542x^55+2544x^56+3684x^57+5586x^58+7116x^59+10958x^60+10164x^61+7368x^62+4846x^63+2148x^64+822x^65+198x^66+210x^67+156x^68+70x^69+48x^70+24x^71+8x^72

The gray image is a linear code over GF(3) with n=270, k=10 and d=156.
This code was found by Heurico 1.16 in 6.26 seconds.