The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+38x^48+152x^51+202x^54+54x^56+226x^57+432x^59+230x^60+1296x^62+298x^63+13122x^64+1728x^65+268x^66+864x^68+238x^69+238x^72+164x^75+80x^78+44x^81+6x^84+2x^87

The gray image is a linear code over GF(3) with n=288, k=9 and d=144.
This code was found by Heurico 1.16 in 1.24 seconds.