The generator matrix

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

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+27x^70+48x^71+107x^72+154x^73+243x^74+200x^75+308x^76+308x^77+396x^78+424x^79+379x^80+410x^81+406x^82+464x^83+436x^84+526x^85+448x^86+514x^87+386x^88+390x^89+287x^90+256x^91+277x^92+200x^93+165x^94+116x^95+112x^96+54x^97+48x^98+24x^99+30x^100+6x^101+19x^102+2x^103+5x^104+8x^106+5x^108+1x^110+2x^112

The gray image is a linear code over GF(2) with n=168, k=13 and d=70.
This code was found by Heurico 1.16 in 15.3 seconds.