The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+24x^54+114x^55+234x^56+392x^57+1170x^58+1014x^59+2038x^60+5424x^61+5766x^62+5920x^63+10470x^64+10020x^65+6138x^66+7188x^67+1716x^68+592x^69+354x^70+156x^71+158x^72+54x^73+42x^74+22x^75+12x^76+6x^77+14x^78+8x^81+2x^87

The gray image is a linear code over GF(3) with n=288, k=10 and d=162.
This code was found by Heurico 1.16 in 3.96 seconds.