The generator matrix

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

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+98x^70+315x^72+493x^74+696x^76+761x^78+890x^80+943x^82+866x^84+852x^86+767x^88+612x^90+406x^92+257x^94+116x^96+59x^98+30x^100+16x^102+6x^104+5x^106+2x^108+1x^112

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 14.8 seconds.