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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 163.

Homogenous weight enumerator: w(x)=1x^0+186x^163+306x^164+26x^165+522x^166+576x^167+252x^168+390x^169+900x^170+1128x^171+1914x^172+2346x^173+2136x^174+3264x^175+2232x^176+1468x^177+306x^178+300x^179+54x^180+264x^181+264x^182+16x^183+216x^184+186x^185+8x^186+90x^187+90x^188+10x^189+102x^190+54x^191+30x^193+30x^194+6x^196+6x^197+2x^198+2x^243

The gray image is a linear code over GF(3) with n=783, k=9 and d=489.
This code was found by Heurico 1.16 in 3.1 seconds.