The generator matrix

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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+206x^171+378x^172+702x^173+946x^174+1098x^175+1296x^176+964x^177+1638x^178+1782x^179+1024x^180+2178x^181+2052x^182+1058x^183+1494x^184+1296x^185+560x^186+468x^187+162x^188+158x^189+36x^190+114x^192+42x^195+20x^198+4x^207+6x^210

The gray image is a linear code over GF(3) with n=810, k=9 and d=513.
This code was found by Heurico 1.16 in 1.89 seconds.