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

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 192.

Homogenous weight enumerator: w(x)=1x^0+222x^192+4x^198+12x^201+4x^207

The gray image is a linear code over GF(3) with n=864, k=5 and d=576.
This code was found by Heurico 1.16 in 1.35 seconds.