The generator matrix

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

generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+97x^68+144x^69+215x^70+274x^71+299x^72+378x^73+380x^74+416x^75+399x^76+504x^77+461x^78+410x^79+430x^80+446x^81+461x^82+370x^83+440x^84+382x^85+342x^86+286x^87+247x^88+244x^89+142x^90+130x^91+103x^92+66x^93+37x^94+28x^95+31x^96+12x^97+9x^98+4x^99+1x^100+1x^102+2x^103

The gray image is a linear code over GF(2) with n=160, k=13 and d=68.
This code was found by Heurico 1.10 in 3.95 seconds.