The generator matrix

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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+44x^51+48x^52+126x^53+442x^54+60x^55+1632x^56+1184x^57+90x^58+5730x^59+1950x^60+132x^61+5832x^62+1824x^63+120x^64+276x^65+88x^66+36x^67+12x^68+36x^69+6x^72+4x^75+4x^78+4x^81+2x^84

The gray image is a linear code over GF(3) with n=270, k=9 and d=153.
This code was found by Heurico 1.16 in 0.46 seconds.