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

generates a code of length 99 over Z3[X]/(X^3) who´s minimum homogenous weight is 186.

Homogenous weight enumerator: w(x)=1x^0+120x^186+132x^187+114x^188+570x^189+276x^190+366x^191+650x^192+354x^193+1164x^194+836x^195+1110x^196+3180x^197+2596x^198+1716x^199+3198x^200+776x^201+414x^202+492x^203+276x^204+114x^205+102x^206+284x^207+90x^208+60x^209+198x^210+84x^211+30x^212+166x^213+48x^214+24x^215+68x^216+24x^217+12x^218+12x^219+12x^220+6x^221+6x^222+2x^273

The gray image is a linear code over GF(3) with n=891, k=9 and d=558.
This code was found by Heurico 1.16 in 3.73 seconds.