The generator matrix

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

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 183.

Homogenous weight enumerator: w(x)=1x^0+586x^183+1446x^184+1698x^185+3058x^186+4236x^187+3204x^188+4610x^189+5178x^190+3900x^191+4586x^192+5844x^193+3294x^194+3712x^195+3936x^196+2256x^197+2282x^198+1998x^199+888x^200+1138x^201+564x^202+276x^203+170x^204+72x^205+24x^206+2x^207+36x^208+14x^210+12x^211+6x^212+2x^213+6x^215+2x^216+6x^217+6x^219

The gray image is a linear code over GF(3) with n=864, k=10 and d=549.
This code was found by Heurico 1.16 in 12.2 seconds.