The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+62x^72+306x^73+418x^74+588x^75+597x^76+772x^77+636x^78+686x^79+589x^80+590x^81+577x^82+540x^83+448x^84+440x^85+293x^86+208x^87+112x^88+144x^89+73x^90+56x^91+31x^92+18x^93+3x^94+2x^95+2x^101

The gray image is a linear code over GF(2) with n=320, k=13 and d=144.
This code was found by Heurico 1.11 in 1.44 seconds.