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

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 186.

Homogenous weight enumerator: w(x)=1x^0+50x^186+48x^188+84x^189+216x^190+36x^191+1100x^192+432x^193+54x^194+98x^195+24x^197+38x^198+4x^201+2x^285

The gray image is a linear code over GF(3) with n=864, k=7 and d=558.
This code was found by Heurico 1.16 in 0.574 seconds.