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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+30x^159+126x^161+206x^162+276x^164+248x^165+108x^166+558x^167+420x^168+864x^169+684x^170+1256x^171+2592x^172+672x^173+2210x^174+3456x^175+732x^176+1542x^177+1728x^178+612x^179+248x^180+384x^182+176x^183+210x^185+98x^186+90x^188+44x^189+18x^191+16x^192+12x^194+22x^195+14x^198+8x^201+10x^204+2x^207+4x^210+2x^213+2x^216+2x^228

The gray image is a linear code over GF(3) with n=783, k=9 and d=477.
This code was found by Heurico 1.16 in 3.45 seconds.