The generator matrix

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

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+750x^161+1136x^162+2232x^163+4224x^164+5656x^165+6192x^166+8544x^167+10356x^168+10998x^169+14166x^170+15032x^171+13824x^172+16722x^173+15274x^174+12960x^175+12414x^176+9846x^177+6228x^178+4632x^179+2774x^180+1386x^181+858x^182+286x^183+126x^184+240x^185+60x^186+84x^188+50x^189+42x^191+24x^192+6x^194+6x^195+6x^197+6x^198+6x^200

The gray image is a linear code over GF(3) with n=774, k=11 and d=483.
This code was found by Heurico 1.16 in 93.4 seconds.