The generator matrix

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

generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+102x^71+159x^72+214x^73+308x^74+322x^75+357x^76+384x^77+422x^78+424x^79+476x^80+420x^81+385x^82+428x^83+408x^84+398x^85+429x^86+444x^87+353x^88+366x^89+297x^90+274x^91+214x^92+146x^93+163x^94+92x^95+70x^96+50x^97+38x^98+24x^99+9x^100+6x^102+2x^103+1x^104+6x^105

The gray image is a linear code over GF(2) with n=166, k=13 and d=71.
This code was found by Heurico 1.10 in 7.38 seconds.