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

generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+68x^68+70x^69+202x^70+200x^71+375x^72+368x^73+479x^74+538x^75+585x^76+668x^77+743x^78+796x^79+811x^80+918x^81+839x^82+990x^83+813x^84+966x^85+858x^86+880x^87+795x^88+700x^89+599x^90+502x^91+436x^92+336x^93+258x^94+172x^95+165x^96+62x^97+97x^98+18x^99+32x^100+8x^101+16x^102+12x^104+2x^106+1x^108+3x^110+1x^112+1x^132

The gray image is a linear code over GF(2) with n=166, k=14 and d=68.
This code was found by Heurico 1.16 in 55.3 seconds.