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

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+138x^183+246x^184+246x^185+490x^186+492x^187+510x^188+1152x^189+942x^190+1032x^191+2032x^192+1956x^193+1410x^194+2706x^195+1740x^196+1164x^197+1324x^198+498x^199+192x^200+248x^201+126x^202+144x^203+170x^204+120x^205+72x^206+94x^207+102x^208+36x^209+86x^210+42x^211+36x^212+24x^213+24x^214+18x^215+36x^216+24x^217+2x^219+6x^220+2x^255

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 3.38 seconds.