The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1 2X  1  1  0  1  1  1  1  1 2X^2+X  0  1  1  1  1  1  0  1  1 2X^2+X 2X^2+X  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X^2+1  1 2X 2X+2  1  0 2X^2+2X+1 2X^2+X+2 X+1  2  1  1 2X+2 2X^2+X+2 2X^2+1 2X^2+X 2X  1  0 2X  1  1 2X^2+X  0
 0  0 2X^2  0  0  0 2X^2 2X^2 X^2 2X^2  0 X^2 X^2  0 X^2  0  0 2X^2 2X^2 2X^2  0 2X^2 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2  0  0  0
 0  0  0 X^2  0  0 2X^2 2X^2  0 X^2 X^2 2X^2 X^2 2X^2  0  0 2X^2 X^2  0 2X^2 2X^2 2X^2 2X^2  0 2X^2  0 2X^2  0 X^2 2X^2 X^2  0
 0  0  0  0 2X^2  0 X^2 2X^2 2X^2 2X^2 X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 2X^2 X^2  0  0 2X^2 X^2 2X^2 2X^2  0 2X^2  0
 0  0  0  0  0 X^2  0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 2X^2  0 X^2 2X^2 X^2 2X^2  0  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+34x^51+54x^53+70x^54+96x^55+456x^56+106x^57+786x^58+1848x^59+2540x^60+3486x^61+5736x^62+9796x^63+6678x^64+8424x^65+9806x^66+4668x^67+3606x^68+76x^69+294x^70+258x^71+64x^72+30x^73+30x^74+56x^75+30x^78+14x^81+4x^84+2x^87

The gray image is a linear code over GF(3) with n=288, k=10 and d=153.
This code was found by Heurico 1.16 in 3.99 seconds.