The generator matrix

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

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+586x^51+1314x^52+4518x^53+8564x^54+12300x^55+24564x^56+36224x^57+50124x^58+70200x^59+83362x^60+82326x^61+72564x^62+48592x^63+21612x^64+10734x^65+3130x^66+438x^67+144x^68+82x^69+42x^70+12x^71+8x^72

The gray image is a linear code over GF(3) with n=270, k=12 and d=153.
This code was found by Heurico 1.16 in 207 seconds.