The generator matrix

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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+264x^172+684x^173+814x^174+1194x^175+1848x^176+1396x^177+1542x^178+1842x^179+1456x^180+1590x^181+1656x^182+1064x^183+1176x^184+1284x^185+620x^186+408x^187+354x^188+214x^189+42x^190+72x^191+4x^192+54x^193+6x^194+10x^195+12x^196+18x^197+6x^198+30x^199+6x^202+12x^203+2x^204+2x^210

The gray image is a linear code over GF(3) with n=810, k=9 and d=516.
This code was found by Heurico 1.16 in 2.09 seconds.