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

generates a code of length 88 over Z3[X]/(X^3) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+78x^162+48x^163+354x^165+114x^166+66x^167+536x^168+156x^169+330x^170+970x^171+720x^172+1248x^173+1760x^174+2172x^175+2322x^176+2128x^177+2160x^178+1668x^179+1274x^180+222x^181+156x^182+318x^183+90x^184+42x^185+246x^186+114x^187+170x^189+36x^190+108x^192+16x^195+22x^198+10x^201+8x^204+12x^207+4x^210+2x^216+2x^237

The gray image is a linear code over GF(3) with n=792, k=9 and d=486.
This code was found by Heurico 1.16 in 3.53 seconds.