The generator matrix

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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+104x^147+126x^148+186x^149+580x^150+354x^151+492x^152+974x^153+1158x^154+1152x^155+1492x^156+2322x^157+2256x^158+1698x^159+2490x^160+1350x^161+908x^162+576x^163+126x^164+276x^165+120x^166+102x^167+284x^168+72x^169+84x^170+134x^171+48x^172+54x^173+84x^174+24x^175+30x^176+12x^177+6x^180+6x^183+2x^207

The gray image is a linear code over GF(3) with n=711, k=9 and d=441.
This code was found by Heurico 1.16 in 2.58 seconds.