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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+78x^166+122x^168+342x^169+18x^170+202x^171+588x^172+180x^173+436x^174+984x^175+720x^176+1332x^177+1938x^178+1440x^179+2302x^180+2316x^181+1440x^182+1706x^183+1470x^184+576x^185+240x^186+444x^187+76x^189+300x^190+50x^192+222x^193+18x^195+30x^196+24x^198+36x^199+16x^201+8x^204+6x^207+2x^210+8x^213+4x^216+2x^219+2x^225+2x^228+2x^234

The gray image is a linear code over GF(3) with n=810, k=9 and d=498.
This code was found by Heurico 1.16 in 15.4 seconds.