The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+264x^55+276x^56+1934x^57+3114x^58+4212x^59+8878x^60+11280x^61+17844x^62+22420x^63+24276x^64+30426x^65+24258x^66+14826x^67+6876x^68+4280x^69+1482x^70+138x^71+176x^72+138x^73+6x^74+16x^75+24x^76+2x^81

The gray image is a linear code over GF(3) with n=288, k=11 and d=165.
This code was found by Heurico 1.16 in 27.7 seconds.