The generator matrix

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

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+354x^170+24x^171+360x^172+390x^173+46x^174+510x^175+1026x^176+204x^177+1878x^178+2412x^179+4572x^180+3258x^181+2268x^182+194x^183+288x^184+282x^185+28x^186+264x^187+162x^188+14x^189+204x^190+150x^191+12x^192+114x^193+132x^194+2x^195+66x^196+78x^197+4x^198+66x^199+36x^200+6x^202+2x^261

The gray image is a linear code over GF(3) with n=810, k=9 and d=507.
This code was found by Heurico 1.16 in 53 seconds.