The generator matrix

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

generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 190.

Homogenous weight enumerator: w(x)=1x^0+30x^190+36x^191+112x^192+12x^193+18x^194+8x^195+12x^196+6x^198+2x^204+2x^207+2x^210+2x^213

The gray image is a linear code over GF(3) with n=288, k=5 and d=190.
This code was found by Heurico 1.13 in 0.245 seconds.