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

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+68x^180+108x^181+348x^182+262x^183+336x^184+582x^185+578x^186+672x^187+1194x^188+672x^189+1902x^190+2826x^191+700x^192+2970x^193+2544x^194+650x^195+918x^196+672x^197+292x^198+114x^199+234x^200+162x^201+120x^202+162x^203+168x^204+54x^205+84x^206+48x^207+66x^208+66x^209+26x^210+12x^211+24x^212+8x^213+12x^214+12x^215+8x^216+6x^217+2x^255

The gray image is a linear code over GF(3) with n=864, k=9 and d=540.
This code was found by Heurico 1.16 in 3.55 seconds.