The generator matrix

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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+468x^166+486x^167+736x^168+1284x^169+1566x^170+1658x^171+1590x^172+1728x^173+1512x^174+1452x^175+1548x^176+1332x^177+1296x^178+1188x^179+702x^180+498x^181+270x^182+108x^183+78x^184+18x^185+18x^186+42x^187+2x^189+24x^190+36x^193+2x^195+24x^196+4x^198+12x^199

The gray image is a linear code over GF(3) with n=783, k=9 and d=498.
This code was found by Heurico 1.16 in 2.07 seconds.