The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+26x^51+24x^53+154x^54+54x^55+108x^56+284x^57+378x^58+168x^59+588x^60+1188x^61+3288x^62+862x^63+2322x^64+6144x^65+922x^66+1728x^67+318x^68+564x^69+108x^70+144x^71+142x^72+54x^73+12x^74+52x^75+28x^78+20x^81+2x^84

The gray image is a linear code over GF(3) with n=288, k=9 and d=153.
This code was found by Heurico 1.16 in 0.886 seconds.