The generator matrix

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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+372x^53+668x^54+2268x^55+2664x^56+3562x^57+7248x^58+6792x^59+7492x^60+11808x^61+6972x^62+4234x^63+3402x^64+1116x^65+290x^66+60x^67+66x^68+32x^69+2x^72

The gray image is a linear code over GF(3) with n=270, k=10 and d=159.
This code was found by Heurico 1.16 in 3.07 seconds.