The generator matrix

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

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+772x^171+600x^172+1998x^173+3946x^174+2622x^175+2988x^176+6692x^177+3306x^178+4074x^179+6998x^180+3234x^181+3828x^182+5590x^183+2394x^184+2478x^185+3778x^186+1032x^187+978x^188+880x^189+360x^190+150x^191+200x^192+42x^193+24x^194+18x^195+12x^196+22x^198+8x^201+12x^204+6x^205+6x^206

The gray image is a linear code over GF(3) with n=810, k=10 and d=513.
This code was found by Heurico 1.16 in 10.8 seconds.