The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 1 X 1 X X 1 1 1 1 0 X 1 X 1 1 0 1 1 0 1 1 X X 1 1 1 1 X 1 0 X 1 X X 1 X X 1 1 1 1 1 X 1 1 1 1 1 0 1 1 1 1 1 1 0 X 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 1 0 X 0 1 X+1 0 X X+1 1 0 X 1 1 0 1 X X 1 1 X+1 1 X+1 0 X X 1 X 1 X+1 X X+1 1 0 X+1 0 1 X 1 0 X+1 X+1 1 X X 1 X X X X+1 0 0 X+1 0 1 1 1 1 1 1 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 X 1 0 X+1 X+1 0 1 1 X+1 1 1 0 X 0 1 1 X+1 X X+1 1 1 0 X X+1 0 1 X+1 1 X X+1 1 X 0 1 X 1 X+1 0 X+1 X X X+1 X+1 0 X+1 X+1 0 X X+1 X+1 0 1 0 X 1 1 0 1 0 1 0
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 1 0 0 1 0 1 0 0 X+1 1 0 X+1 0 0 X 1 1 1 X+1 0 1 1 X X+1 X+1 X+1 1 X+1 0 X+1 X+1 1 X X+1 X+1 1 1 0 X 0 1 X 0 X+1 0 X 1 0 X X+1 0 X+1 1 1 X+1 X 0 0
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 X 0 0 X+1 1 1 X 1 X 1 1 X X X+1 X+1 0 X+1 1 X+1 X 0 0 0 1 X+1 X 0 X 0 1 X+1 X 0 X+1 X+1 1 X+1 0 1 X+1 0 1 1 0 X X X+1 1 X 1 X+1 0 0 X 0 X X+1 X 1 X 0
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X X X 0 X 0 X X 0 X 0 X 0 0 X X X 0 X 0 0 0 X X X X X X 0 0 0 0 X X X X 0 X 0 X X 0 0 X 0 0 X 0 X 0 0 X X X X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X X 0 0 X X 0 0 X 0 0 X 0 X X 0 X 0 X X 0 X X 0 X X 0 0 X 0 X 0 0 0 0 0 X 0 X X 0 X 0 X X X 0 X 0 0 X X 0 X 0 X 0 X 0
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X 0 X X X X X X X X X 0 0 0 X X X X 0 X 0 0 X X 0 X X X X 0 X X X 0 0 X 0 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+72x^70+80x^71+159x^72+220x^73+274x^74+308x^75+337x^76+380x^77+397x^78+454x^79+439x^80+438x^81+407x^82+444x^83+434x^84+442x^85+418x^86+394x^87+315x^88+334x^89+291x^90+242x^91+265x^92+174x^93+156x^94+104x^95+78x^96+56x^97+27x^98+22x^99+18x^100+4x^101+4x^102+1x^106+2x^108+1x^110
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 13.5 seconds.