The generator matrix

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

generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+64x^70+102x^71+179x^72+194x^73+259x^74+300x^75+345x^76+382x^77+425x^78+438x^79+402x^80+436x^81+427x^82+442x^83+417x^84+458x^85+405x^86+430x^87+344x^88+318x^89+295x^90+236x^91+247x^92+214x^93+122x^94+86x^95+93x^96+44x^97+41x^98+14x^99+15x^100+2x^101+6x^102+5x^104+2x^106+1x^110+1x^118

The gray image is a linear code over GF(2) with n=166, k=13 and d=70.
This code was found by Heurico 1.16 in 14 seconds.