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

generates a code of length 91 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+390x^171+1004x^174+162x^176+1286x^177+162x^178+1458x^179+2892x^180+648x^181+2430x^182+4354x^183+648x^184+1782x^185+958x^186+530x^189+394x^192+310x^195+184x^198+62x^201+20x^204+6x^207+2x^252

The gray image is a linear code over GF(3) with n=819, k=9 and d=513.
This code was found by Heurico 1.16 in 3.34 seconds.