The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  X  1  1  1  1  X  0  0  1  1  0  1  X  X  1  X  1  X  1  1  1  1  0  X  1  1  1  1  X  1  1  1  1  X  1  1  0  0  0  X  1  1  X  X  0  1  1  0  1  0  1  1  1  X  0  X  1  1  1  0  1  1  1  1  X  1  1
 0  1  0  1  0  1  1  0  0  1 X+1  1  X  1  0  X  1 X+1  1  1  X  1  1  1  0  0  1  X  1  0  1 X+1 X+1  1  X  1  1  1  1  0  0  X  0 X+1  1  X  1  0 X+1  X  1  1  0  1  0  1  0  1  0 X+1  1  X  X  1  0  X  0  1  0  0  1  X  1  X X+1 X+1  1  1  0  0
 0  0  1  1  1  0  1  0  1  1  0  X  1 X+1 X+1  X X+1  0  1  0  1  1  0  1  X  1  X  1  0  X X+1  X  X  1 X+1  0  X  1 X+1  1  X  1  0  1  X X+1  X  1  X  1  0  X  1 X+1  X  1  1 X+1  0 X+1  0  X  1  0 X+1 X+1  1  0  1  X  1  1 X+1  X  1  X  X X+1  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  X  0  X  X  X  0  X  0  X  X  X  0  X  X  X  X  0  0  X  X  X  0  0  0  X  0  0  X  X  0  0  0  0  X  X  0  X  X  X  0  0  0  0  0  0  0  X  X  0  X  0  0  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  X  0  0  X  0  0  X  X  0  X  0  X  X  X  X  0  0  0  0  X  0  0  X  X  X  0  X  X  0  X  X  X  X  0  X  0  X  0  0  X  0  X  0  X  0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  0  0  X  X  X  X  X  X  X  X  X  X  0  X  X  0  X  0  X  0  0  X  X  0  0  X  0  0  X  X  X  X  0  X  0  0  0  0  X  X  X  X  0  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  X  0  0  X  0  X  X  0  X  X  X  X  X  X  0  X  X  0  0  X  0  0  X  X  0  X  X  0  X  0  X  0  0  X  X  0  X  0  X  0  X  0  0  X  0  X  0  X  X  0  0  X  0  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  0  0  X  X  0  0  0  X  X  X  0  X  X  X  0  0  X  X  X  0  X  X  0  X  X  0  X  X  X  X  0  0  X  X  X  X  X  X  0  0  X  X  0  X  0  X  0  0  X  X  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  0  X  X  0  0  0  X  0  X  X  0  0  0  0  0  X  0  X  X  0  X  X  0  X  X  0  0  0  X  0  X  X  X  0  0  X  X  0  X  0  X  0  0  0  0  X  X  X  0  X  X  X  X  0  0  0  X  X  X  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  X  0  X  X  X  0  0  0  X  X  0  0  X  X  0  0  0  X  X  X  0  0  X  0  X  X  0  X  0  0  0  0  0  X  X  X  X  0  X  0  X  0  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  0  0  0  X  X  X

generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+24x^66+36x^67+105x^68+130x^69+223x^70+232x^71+309x^72+302x^73+348x^74+380x^75+415x^76+450x^77+422x^78+534x^79+461x^80+528x^81+482x^82+412x^83+366x^84+406x^85+335x^86+324x^87+242x^88+174x^89+149x^90+116x^91+95x^92+54x^93+40x^94+14x^95+40x^96+4x^97+20x^98+11x^100+4x^102+3x^104+1x^106

The gray image is a linear code over GF(2) with n=160, k=13 and d=66.
This code was found by Heurico 1.16 in 14 seconds.