The generator matrix

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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+74x^54+144x^55+480x^56+412x^57+378x^58+1410x^59+700x^60+756x^61+1440x^62+472x^63+180x^64+42x^65+32x^66+30x^68+2x^69+2x^72+6x^75

The gray image is a linear code over GF(3) with n=270, k=8 and d=162.
This code was found by Heurico 1.16 in 0.0567 seconds.