The generator matrix

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

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+214x^51+306x^52+1614x^53+2236x^54+5004x^55+8634x^56+10302x^57+18156x^58+22932x^59+25928x^60+31284x^61+24060x^62+13764x^63+7722x^64+3786x^65+658x^66+204x^67+198x^68+102x^69+18x^70+12x^71+10x^72+2x^75

The gray image is a linear code over GF(3) with n=270, k=11 and d=153.
This code was found by Heurico 1.16 in 25.5 seconds.