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

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+156x^163+276x^164+126x^165+546x^166+570x^167+186x^168+642x^169+1350x^170+856x^171+1194x^172+2526x^173+2770x^174+2046x^175+2976x^176+930x^177+546x^178+492x^179+106x^180+288x^181+234x^182+68x^183+174x^184+168x^185+30x^186+120x^187+78x^188+18x^189+66x^190+42x^191+4x^192+42x^193+30x^194+6x^195+6x^196+6x^197+6x^199+2x^237

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 2.95 seconds.