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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 149.

Homogenous weight enumerator: w(x)=1x^0+276x^149+276x^150+108x^151+720x^152+118x^153+486x^154+1488x^155+58x^156+648x^157+1482x^158+126x^159+216x^160+192x^161+26x^162+72x^164+12x^165+96x^167+96x^168+24x^170+6x^171+24x^173+6x^177+2x^180+2x^210

The gray image is a linear code over GF(3) with n=702, k=8 and d=447.
This code was found by Heurico 1.16 in 89.6 seconds.