The generator matrix

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

generates a code of length 91 over Z3[X]/(X^3) who´s minimum homogenous weight is 173.

Homogenous weight enumerator: w(x)=1x^0+150x^173+432x^174+468x^175+1470x^176+1116x^177+846x^178+1458x^179+1292x^180+846x^181+2394x^182+1844x^183+1314x^184+2124x^185+1356x^186+774x^187+888x^188+382x^189+126x^190+150x^191+70x^192+78x^194+42x^195+30x^197+8x^198+6x^200+4x^201+4x^204+8x^210+2x^231

The gray image is a linear code over GF(3) with n=819, k=9 and d=519.
This code was found by Heurico 1.16 in 1.96 seconds.