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

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+150x^171+174x^172+306x^173+454x^174+342x^175+516x^176+522x^177+540x^178+972x^179+1884x^180+1782x^181+4242x^182+3010x^183+1458x^184+1242x^185+400x^186+204x^187+138x^188+206x^189+120x^190+186x^191+134x^192+120x^193+102x^194+150x^195+66x^196+24x^197+78x^198+48x^199+18x^200+44x^201+6x^202+30x^203+12x^204+2x^258

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 3.07 seconds.