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

generates a code of length 97 over Z3[X]/(X^3) who´s minimum homogenous weight is 183.

Homogenous weight enumerator: w(x)=1x^0+416x^183+1110x^186+72x^187+162x^188+1498x^189+576x^190+972x^191+2334x^192+1728x^193+1944x^194+2544x^195+1818x^196+1296x^197+1514x^198+180x^199+468x^201+462x^204+258x^207+184x^210+96x^213+48x^216+2x^261

The gray image is a linear code over GF(3) with n=873, k=9 and d=549.
This code was found by Heurico 1.16 in 3.62 seconds.