The generator matrix

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

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+284x^183+180x^184+792x^185+1176x^186+900x^187+1602x^188+1296x^189+810x^190+2196x^191+1356x^192+1062x^193+2448x^194+1146x^195+1152x^196+1476x^197+870x^198+270x^199+234x^200+210x^201+124x^204+84x^207+4x^210+4x^216+2x^225+2x^231+2x^234

The gray image is a linear code over GF(3) with n=864, k=9 and d=549.
This code was found by Heurico 1.16 in 2.09 seconds.