The generator matrix

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

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+116x^51+108x^52+192x^53+682x^54+204x^55+864x^56+1340x^57+822x^58+2952x^59+5078x^60+1368x^61+2982x^62+1622x^63+264x^64+216x^65+506x^66+132x^67+72x^68+110x^69+18x^70+12x^71+8x^72+8x^75+6x^78

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 0.789 seconds.