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

generates a code of length 91 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+108x^168+90x^170+344x^171+66x^172+150x^173+554x^174+132x^175+216x^176+1342x^177+708x^178+216x^179+3152x^180+2268x^181+204x^182+3802x^183+2334x^184+186x^185+2184x^186+210x^187+144x^188+334x^189+96x^190+114x^191+248x^192+18x^193+78x^194+134x^195+36x^197+94x^198+18x^200+50x^201+6x^203+12x^204+4x^207+6x^210+14x^213+4x^216+2x^219+2x^222+2x^240

The gray image is a linear code over GF(3) with n=819, k=9 and d=504.
This code was found by Heurico 1.16 in 3.71 seconds.