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

generates a code of length 88 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+226x^165+156x^166+126x^167+672x^168+432x^169+534x^170+542x^171+822x^172+1896x^173+488x^174+1788x^175+4962x^176+508x^177+1782x^178+2376x^179+346x^180+540x^181+120x^182+272x^183+150x^184+90x^185+198x^186+66x^187+60x^188+200x^189+60x^190+36x^191+140x^192+30x^193+6x^194+44x^195+6x^196+6x^201+2x^237

The gray image is a linear code over GF(3) with n=792, k=9 and d=495.
This code was found by Heurico 1.16 in 3.13 seconds.