The generator matrix

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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+222x^165+198x^166+810x^167+970x^168+810x^169+1674x^170+1288x^171+900x^172+2052x^173+1626x^174+1134x^175+2430x^176+1594x^177+1026x^178+1566x^179+532x^180+288x^181+216x^182+154x^183+18x^184+96x^186+54x^189+12x^192+2x^195+6x^198+2x^204+2x^210

The gray image is a linear code over GF(3) with n=783, k=9 and d=495.
This code was found by Heurico 1.16 in 1.81 seconds.