The generator matrix

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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+58x^165+102x^167+264x^168+132x^169+678x^170+810x^171+792x^172+2238x^173+1614x^174+1926x^175+4254x^176+3008x^177+3318x^178+7140x^179+4750x^180+4362x^181+7704x^182+4106x^183+3030x^184+4206x^185+1326x^186+912x^187+1296x^188+494x^189+84x^190+42x^191+148x^192+12x^193+24x^194+98x^195+12x^196+12x^197+28x^198+6x^200+16x^201+14x^204+6x^207+10x^210+4x^213+4x^216+4x^219+2x^222+2x^228

The gray image is a linear code over GF(3) with n=810, k=10 and d=495.
This code was found by Heurico 1.16 in 14.6 seconds.