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

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 190.

Homogenous weight enumerator: w(x)=1x^0+90x^190+378x^191+10x^192+198x^194+6x^195+18x^197+2x^198+18x^199+2x^201+4x^204+2x^213

The gray image is a linear code over GF(3) with n=864, k=6 and d=570.
This code was found by Heurico 1.16 in 3.9 seconds.