The generator matrix

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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+348x^145+1050x^146+2156x^147+3702x^148+4884x^149+6174x^150+7908x^151+10212x^152+12330x^153+13896x^154+14910x^155+17234x^156+15636x^157+15534x^158+15270x^159+11952x^160+8808x^161+6254x^162+4158x^163+2490x^164+992x^165+492x^166+294x^167+60x^168+138x^169+78x^170+18x^171+66x^172+36x^173+12x^174+24x^175+24x^176+6x^177

The gray image is a linear code over GF(3) with n=702, k=11 and d=435.
This code was found by Heurico 1.16 in 83.6 seconds.