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

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 181.

Homogenous weight enumerator: w(x)=1x^0+180x^181+288x^182+118x^183+450x^184+606x^185+200x^186+810x^187+1158x^188+532x^189+1794x^190+2832x^191+1902x^192+2634x^193+3000x^194+714x^195+738x^196+264x^197+76x^198+210x^199+204x^200+26x^201+204x^202+150x^203+38x^204+120x^205+138x^206+24x^207+102x^208+60x^209+6x^210+42x^211+24x^212+6x^214+24x^215+6x^216+2x^267

The gray image is a linear code over GF(3) with n=864, k=9 and d=543.
This code was found by Heurico 1.16 in 3.33 seconds.