The generator matrix

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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 169.

Homogenous weight enumerator: w(x)=1x^0+276x^169+444x^170+702x^171+1356x^172+1944x^173+2616x^174+2472x^175+3000x^176+4918x^177+3978x^178+4920x^179+5934x^180+4230x^181+4680x^182+5284x^183+3234x^184+2730x^185+2580x^186+1416x^187+876x^188+458x^189+210x^190+156x^191+70x^192+144x^193+126x^194+18x^195+120x^196+42x^197+6x^198+36x^199+24x^200+4x^201+18x^202+12x^203+8x^204+6x^205

The gray image is a linear code over GF(3) with n=810, k=10 and d=507.
This code was found by Heurico 1.16 in 13.8 seconds.