The generator matrix

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

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+636x^136+1212x^137+3962x^138+6078x^139+8844x^140+13688x^141+18720x^142+21846x^143+30228x^144+35322x^145+39510x^146+50374x^147+52872x^148+48960x^149+50170x^150+44946x^151+34086x^152+28142x^153+18540x^154+10326x^155+7086x^156+3318x^157+1332x^158+672x^159+252x^160+48x^161+84x^162+96x^163+36x^164+12x^165+12x^166+12x^167+18x^168

The gray image is a linear code over GF(3) with n=666, k=12 and d=408.
This code was found by Heurico 1.16 in 601 seconds.