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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+12x^73+36x^74+74x^75+94x^76+88x^77+88x^78+68x^79+31x^80+12x^81+3x^82+2x^83+2x^84+1x^146

The gray image is a linear code over GF(2) with n=308, k=9 and d=146.
This code was found by Heurico 1.16 in 0.242 seconds.