The generator matrix

0 1 0 1 1 X 0 1 1 1 X 0 0 1 X 1 1 0 0 1 1 X X 1 X 1 0 X 0 1 1 X X X 0 1 X 1 X 0 1 1 1 1 1 X 0 1 X 1 0 1 1 1 1 X 0 X 1 X 0 1 1 1 1 1 0 1 X 1 X 1 1 X 1 1 1 1 0 X 1 1 1
1 1 1 1 0 0 0 X 1 0 1 0 1 0 0 1 X 1 1 0 0 0 1 1 0 1 X X 1 X+1 1 0 X 0 X 0 X 0 1 1 X X+1 X 1 0 X X X+1 X 1 1 X+1 X+1 0 X+1 1 1 1 1 1 1 0 1 X+1 1 1 0 X 1 0 0 X+1 X 0 0 1 X X 0 X X 1 0
0 0 1 X+1 X+1 1 0 X X+1 X+1 0 0 1 0 1 0 X 0 X X+1 1 1 X+1 X+1 0 1 1 X 1 0 X+1 1 1 X 0 0 X 0 0 1 0 1 1 X 0 0 1 X 1 X X X X X 0 X+1 1 1 0 X+1 X+1 1 1 1 X+1 0 1 X X 0 0 0 1 1 X X X 1 X 1 X X 0
0 0 1 X+1 X+1 1 X 0 X X X+1 1 0 1 X 1 X 0 1 X X+1 1 X+1 1 1 X 0 0 0 1 0 1 1 1 0 X+1 0 0 X X X 0 X+1 0 X+1 X 0 X X+1 0 0 1 1 0 0 0 1 X+1 0 X X+1 1 0 0 1 0 X+1 X+1 X+1 1 0 1 X 1 X+1 X+1 X X+1 1 1 0 0 0
0 0 0 X X+1 X+1 1 X+1 0 X+1 X 1 0 1 X+1 X 1 0 0 X+1 1 1 0 X 1 X X+1 1 0 0 X X+1 1 1 1 1 1 X+1 0 X X+1 0 X+1 X X X X X+1 0 X+1 X+1 X+1 1 0 0 X+1 X+1 1 X+1 X+1 X X 1 1 X+1 1 X 1 X+1 X+1 X X 1 0 0 1 X+1 1 0 X X+1 X 0
0 0 0 0 0 0 X X X+1 X+1 1 1 1 1 X+1 X+1 X X X+1 X+1 X 0 X X X+1 X+1 X+1 X 1 0 0 1 X+1 0 1 0 X+1 1 1 X X+1 X X+1 X+1 X 1 0 X 0 X+1 X+1 X 0 X X+1 1 1 0 0 1 X+1 1 X+1 0 1 1 0 0 0 0 1 1 0 X+1 X+1 X+1 X 1 0 X+1 0 0 0
0 0 0 0 X X X X X 0 X 0 X 0 X 0 0 X 0 X 0 0 X X X 0 0 0 0 0 0 X 0 0 X X 0 0 X 0 X X X 0 0 X X X 0 0 X 0 X 0 0 0 X 0 0 X X X X 0 X X X 0 X X X 0 0 0 0 X X X X 0 0 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+48x^70+78x^71+166x^72+232x^73+283x^74+302x^75+330x^76+414x^77+356x^78+398x^79+451x^80+428x^81+470x^82+470x^83+448x^84+422x^85+408x^86+406x^87+313x^88+326x^89+298x^90+284x^91+248x^92+176x^93+151x^94+84x^95+73x^96+46x^97+33x^98+24x^99+17x^100+4x^101+1x^102+2x^103+1x^108

The gray image is a linear code over GF(2) with n=166, k=13 and d=70.
This code was found by an older version of Heurico in 0 seconds.