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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+434x^147+54x^148+144x^149+600x^150+486x^151+216x^152+856x^153+1296x^154+432x^155+704x^156+594x^157+180x^158+210x^159+170x^162+62x^165+72x^168+42x^171+6x^174+2x^207

The gray image is a linear code over GF(3) with n=693, k=8 and d=441.
This code was found by Heurico 1.16 in 3.72 seconds.