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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+24x^72+2x^73+42x^74+50x^75+76x^76+108x^77+75x^78+76x^79+27x^80+18x^81+10x^82+2x^83+1x^142

The gray image is a linear code over GF(2) with n=308, k=9 and d=144.
This code was found by Heurico 1.16 in 0.32 seconds.