The generator matrix

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

generates a code of length 33 over Z3[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+226x^57+366x^58+1944x^59+3552x^60+4326x^61+8850x^62+11750x^63+14742x^64+26256x^65+26038x^66+22512x^67+27528x^68+15634x^69+7320x^70+3804x^71+1632x^72+270x^73+132x^74+212x^75+36x^76+12x^77+2x^78+2x^84

The gray image is a linear code over GF(3) with n=297, k=11 and d=171.
This code was found by Heurico 1.16 in 28.9 seconds.