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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+124x^165+132x^166+260x^168+648x^169+272x^171+1248x^172+232x^174+3456x^175+318x^177+6144x^178+256x^180+4338x^181+300x^183+912x^184+180x^186+324x^187+72x^189+192x^190+76x^192+90x^193+36x^195+12x^196+12x^198+16x^201+12x^204+4x^207+8x^210+2x^213+4x^216+2x^231

The gray image is a linear code over GF(3) with n=801, k=9 and d=495.
This code was found by Heurico 1.16 in 7.08 seconds.