The generator matrix

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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+306x^168+600x^169+1596x^170+2800x^171+4236x^172+4704x^173+6374x^174+9036x^175+9240x^176+12144x^177+14430x^178+12582x^179+14714x^180+17196x^181+14154x^182+13744x^183+12672x^184+8670x^185+6680x^186+4644x^187+2442x^188+1890x^189+1152x^190+342x^191+264x^192+144x^193+114x^194+82x^195+18x^196+66x^197+26x^198+24x^199+24x^200+12x^201+12x^203+12x^204

The gray image is a linear code over GF(3) with n=810, k=11 and d=504.
This code was found by Heurico 1.16 in 97.9 seconds.