The generator matrix

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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+372x^171+432x^172+2274x^173+2072x^174+894x^175+2676x^176+1910x^177+690x^178+1824x^179+1244x^180+558x^181+1596x^182+956x^183+348x^184+582x^185+506x^186+120x^187+444x^188+144x^189+36x^190+2x^192+2x^204

The gray image is a linear code over GF(3) with n=801, k=9 and d=513.
This code was found by Heurico 1.16 in 1.31 seconds.