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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+540x^161+536x^162+3324x^163+4974x^164+7006x^165+12084x^166+14538x^167+18758x^168+24714x^169+28800x^170+32652x^171+41340x^172+43956x^173+42810x^174+52872x^175+45294x^176+39452x^177+36966x^178+28308x^179+19386x^180+15114x^181+8466x^182+4452x^183+2700x^184+1362x^185+392x^186+318x^187+108x^188+18x^189+90x^190+54x^191+2x^192+6x^193+6x^194+6x^195+12x^196+6x^197+12x^198+6x^200

The gray image is a linear code over GF(3) with n=783, k=12 and d=483.
This code was found by Heurico 1.16 in 711 seconds.