The generator matrix

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

generates a code of length 84 over Z3[X]/(X^3) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+1248x^156+2250x^157+4428x^158+8136x^159+10728x^160+14094x^161+18284x^162+24858x^163+29502x^164+33348x^165+42156x^166+43236x^167+45666x^168+50292x^169+47592x^170+39966x^171+37800x^172+27414x^173+20388x^174+12942x^175+7902x^176+4680x^177+2592x^178+792x^179+780x^180+90x^181+204x^183+54x^186+18x^189

The gray image is a linear code over GF(3) with n=756, k=12 and d=468.
This code was found by Heurico 1.16 in 692 seconds.