The generator matrix

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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 173.

Homogenous weight enumerator: w(x)=1x^0+492x^173+1136x^174+108x^175+984x^176+1002x^177+144x^178+558x^179+642x^180+36x^181+438x^182+440x^183+36x^184+270x^185+252x^186+6x^194+6x^198+6x^200+2x^201+2x^207

The gray image is a linear code over GF(3) with n=801, k=8 and d=519.
This code was found by Heurico 1.16 in 0.462 seconds.