The generator matrix

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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+52x^45+160x^48+222x^51+54x^52+228x^54+432x^55+262x^57+1296x^58+13444x^60+1728x^61+262x^63+864x^64+274x^66+202x^69+132x^72+60x^75+10x^78

The gray image is a linear code over GF(3) with n=270, k=9 and d=135.
This code was found by Heurico 1.16 in 1.15 seconds.