The generator matrix

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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+756x^140+1482x^141+3900x^142+6498x^143+9366x^144+14916x^145+17250x^146+22824x^147+29022x^148+34584x^149+41896x^150+48090x^151+50892x^152+51484x^153+49212x^154+42018x^155+34722x^156+28902x^157+18294x^158+11928x^159+6972x^160+3864x^161+1408x^162+624x^163+246x^164+60x^165+72x^166+36x^167+20x^168+24x^169+18x^170+6x^171+30x^172+12x^173+6x^174+6x^176

The gray image is a linear code over GF(3) with n=684, k=12 and d=420.
This code was found by Heurico 1.16 in 618 seconds.