The generator matrix

 1  0  1  1  1  1  1  1 2X^2  1  1  0  1  1  1 2X^2  1  1  1  1  X  1  1  1 2X  1  1  1 2X^2+X  1  1 2X  1  1  1  1  1  1  1 2X^2+X  1  1  1  1  1  X  0  X  1  1  1 X^2+2X  1  1  1  1  1  1  1 2X  1  1  1 2X^2+X X^2+2X  1  1  1  1  1  1  1  1  1  1 X^2+X X^2+2X 2X^2  X  0  1  1 2X^2 2X^2+2X  1  1  1  1  1 2X 2X^2 X^2+2X X^2  1  1  1
 0  1  1  2 2X^2 2X^2+2  0 2X+1  1 X^2+1  2  1 X+1 2X^2 X^2+2  1  1 X^2+1 2X^2 2X^2+X+2  1  0 2X+2 2X^2+X  1 2X X^2+2X+1 X+2  1 X^2+2X+2 X^2+2X+1  1 X+2 X+1 2X^2+X+1 X^2+2X+2 2X^2+X 2X^2+2X 2X^2+X+2  1 2X 2X^2+1 2X+1 2X^2+2 X^2+X  1  1  1 2X^2+X+1 2X+1 X^2+X  1 X^2+2X 2X^2+2 X+1 2X^2+1 2X^2+X+2  X X^2+2X  1 2X^2+X+2 2X^2+2X X^2+2X  1  1  X X^2+2  2 X^2+X+2 X+2 2X^2  0 2X^2+2X+2 2X X^2+2X+2  1  1  1  1  1 2X^2+X 2X^2+2X  1  1 2X^2+X  0  X 2X^2+2X+2 2X^2+2X+2  1  1  1  1  1 2X^2+2 X^2
 0  0 2X X^2 X^2+X 2X^2+X X^2+2X  X  X 2X^2+2X X^2+2X X^2+2X X^2 2X^2  X 2X^2+2X X^2+X X^2 2X^2+X X^2  X 2X^2+2X 2X  0  0 2X^2 2X^2+2X  X 2X^2 2X^2  0 X^2+X X^2+2X  X 2X 2X^2+X 2X^2+2X X^2+X 2X^2 2X^2+2X X^2+2X  0 X^2+X 2X 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+X X^2 X^2+2X X^2+2X  X X^2+X  0 2X^2+X X^2+X  X 2X^2+2X 2X^2+2X 2X^2+X X^2 2X^2 X^2  X X^2  0 2X^2 2X^2+2X 2X 2X  X 2X^2+2X 2X  0  0 2X X^2 2X 2X^2+X 2X^2 2X^2+X X^2+X X^2 X^2+2X X^2 2X X^2+2X X^2+X 2X^2 2X 2X^2+X  0  X X^2+2X 2X^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+212x^186+216x^187+780x^188+1130x^189+504x^190+576x^191+712x^192+234x^193+432x^194+464x^195+192x^196+336x^197+336x^198+144x^199+144x^200+120x^201+14x^204+6x^205+4x^207+2x^216+2x^237

The gray image is a linear code over GF(3) with n=864, k=8 and d=558.
This code was found by Heurico 1.16 in 0.574 seconds.