The generator matrix

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

generates a code of length 88 over Z3[X]/(X^3) who´s minimum homogenous weight is 163.

Homogenous weight enumerator: w(x)=1x^0+420x^163+972x^164+3432x^165+4866x^166+7932x^167+11728x^168+13884x^169+18672x^170+24458x^171+29148x^172+32274x^173+42492x^174+42078x^175+46278x^176+48976x^177+44778x^178+40782x^179+38348x^180+26574x^181+19596x^182+14670x^183+8862x^184+4956x^185+2896x^186+1242x^187+504x^188+274x^189+132x^190+24x^191+30x^192+30x^193+54x^194+30x^195+18x^196+18x^198+12x^199

The gray image is a linear code over GF(3) with n=792, k=12 and d=489.
This code was found by Heurico 1.16 in 729 seconds.