The generator matrix

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

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+24x^69+74x^70+176x^71+248x^72+356x^73+452x^74+432x^75+539x^76+626x^77+681x^78+744x^79+777x^80+804x^81+850x^82+920x^83+969x^84+892x^85+877x^86+872x^87+814x^88+806x^89+679x^90+640x^91+498x^92+410x^93+359x^94+248x^95+200x^96+144x^97+94x^98+56x^99+41x^100+32x^101+21x^102+8x^103+8x^104+2x^105+4x^106+1x^108+4x^110+1x^122

The gray image is a linear code over GF(2) with n=168, k=14 and d=69.
This code was found by Heurico 1.16 in 99.5 seconds.