The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  0  1  1  1  1  0  1  X  1  X  1  0  1  1  X  1  0  1  0  1  0  0  1  1  0  X  0  1  X  1  1  1  X  0  1  1  1  0  0  0  0  1  X  1  X  0  X  1  0  1  1  1  X  1  0  X  1  1  1  X  1  1  X  1  0
 0  1  0  0  0  1  1  1  0  0 X+1 X+1  1  X  1  X X+1  0  1  1  0  1  X  X  0  1  X X+1  1 X+1  X X+1  0  1  1  1  1  0  1  0  0  0  0 X+1  1  0  1  1  X  1  1  X  1  1  X  X  0  1  1  0  0  X  1 X+1  1  X  X  1  1  0 X+1  0  X  1  X  0  X X+1  1
 0  0  1  0  1  1  0  1  0  1  1  0  0  1 X+1 X+1  X  0  1 X+1 X+1  X  0  1  0  0  0  X X+1  X  1  1  0 X+1  X  0  1 X+1 X+1  0  1  1  1  X  1  1 X+1  1 X+1  1 X+1  1  X X+1  X  1  1  1  0  0  1  0 X+1  0  X  0  1  X X+1  1  1  0 X+1  1  1  X  1 X+1  X
 0  0  0  1  1  0  1  1  1  0  1  X  1  1  0  X  1 X+1  X X+1  1  1  0  0 X+1  0  0 X+1  X  0  1  1  1  X X+1  X  X X+1  X  1  0  0 X+1  X  1  1  0  X  0  1 X+1  X  0  1  1  1  0  X  X  1  X  1 X+1  X X+1  1  0 X+1 X+1 X+1  X  1  0  0  X  X X+1  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  X  0  0  0  X  X  X  X  0  X  X  X  X  0  0  X  X  X  0  X  0  0  X  0  X  X  X  0  0  X  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  X  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  X  0  X  0  0  X  X  X  0  0  X  X  0  0  0  0  X  X  0  X  X  0  0  X  X  X  0  X  0  0  X  X  X  X  0  X  0  X  X  0  0  X  X  0  0  0  X  0  0  X  0  X  0  0  X  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  X  0  X  0  0  X  0  X  X  0  X  X  0  X  X  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  X  0  0  X  0  0  X  X  0  X  0  0  X  0  X  X  0  X  0  X  X  0  0  0  0  0  0  X  X  0  0  X  0  0  X  0  X  X  0  X  0  X  X  0  0  X  0  0  X  X  0  0  X  0  X  X  X  0  0  X  0  0  X  X  X  X  0  X
 0  0  0  0  0  0  0  0  X  0  X  0  0  0  0  X  0  0  0  0  X  X  X  X  0  X  0  X  0  X  0  X  0  X  X  X  0  0  X  X  X  0  X  X  X  0  X  0  X  0  X  0  X  X  X  X  X  X  0  0  0  X  0  X  0  X  0  0  0  0  X  X  0  X  0  X  0  X  X
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  X  0  0  X  0  X  X  X  0  X  0  X  0  X  0  X  0  X  0  X  X  0  X  X  X  0  0  0  X  X  0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  0  X  0  X  X  0  X  0  0  X  0  0  X  X  0  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+74x^65+144x^66+222x^67+310x^68+362x^69+481x^70+502x^71+601x^72+682x^73+733x^74+776x^75+875x^76+968x^77+978x^78+978x^79+990x^80+950x^81+892x^82+894x^83+716x^84+666x^85+569x^86+522x^87+454x^88+318x^89+231x^90+172x^91+107x^92+68x^93+48x^94+30x^95+30x^96+8x^97+14x^98+8x^100+4x^102+3x^104+2x^106+1x^112

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 64.2 seconds.