The generator matrix

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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+50x^65+122x^66+218x^67+283x^68+394x^69+525x^70+528x^71+608x^72+698x^73+765x^74+868x^75+881x^76+860x^77+902x^78+954x^79+1003x^80+982x^81+857x^82+790x^83+789x^84+670x^85+562x^86+520x^87+414x^88+346x^89+299x^90+188x^91+91x^92+92x^93+58x^94+30x^95+20x^96+4x^97+5x^98+4x^100+1x^102+1x^104+1x^120

The gray image is a linear code over GF(2) with n=158, k=14 and d=65.
This code was found by Heurico 1.16 in 91.8 seconds.