The generator matrix

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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+68x^62+54x^63+185x^64+140x^65+278x^66+312x^67+452x^68+482x^69+590x^70+656x^71+710x^72+882x^73+874x^74+948x^75+983x^76+1084x^77+965x^78+1124x^79+819x^80+900x^81+748x^82+704x^83+590x^84+474x^85+402x^86+240x^87+252x^88+122x^89+119x^90+52x^91+67x^92+8x^93+37x^94+6x^95+33x^96+4x^97+12x^98+4x^100+2x^102+1x^106

The gray image is a linear code over GF(2) with n=154, k=14 and d=62.
This code was found by Heurico 1.16 in 90.4 seconds.