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  1  1  X  X  1  1  X  1
 0 X^2  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 2X^2 X^2  0 2X^2 X^2 X^2 2X^2
 0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2  0  0 2X^2 X^2 2X^2 2X^2  0 2X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2  0
 0  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0  0 2X^2 X^2 X^2 2X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 2X^2 2X^2  0  0 2X^2
 0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2  0 2X^2 2X^2 X^2  0 X^2  0  0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2  0 2X^2 2X^2 2X^2 X^2  0 2X^2  0  0 2X^2 X^2  0 X^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+156x^51+178x^54+324x^57+5208x^60+504x^63+132x^69+42x^72+12x^78+4x^81

The gray image is a linear code over GF(3) with n=270, k=8 and d=153.
This code was found by Heurico 1.16 in 68.1 seconds.