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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+237x^72+112x^75+247x^76+256x^77+320x^79+229x^80+224x^81+80x^83+175x^84+32x^85+107x^88+25x^92+2x^96+1x^132

The gray image is a linear code over GF(2) with n=316, k=11 and d=144.
This code was found by Heurico 1.16 in 31.8 seconds.