The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  0  1  1  0  1  1  0  1  0  1  1  1  1  0  1  1  0  1  0  1  1  1  0  0  1  X  1  1  X  1  1  1  1  X  1  1  0  1  1  1  X  1  0  1  1  1  1  1  1  1  X  1  1  X  X  1  1  X  1  1  0  X  0  1  1  X  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  X X+1  1  0  1 X+1  X  1 X+1  1  1  0  1 X+1  0 X+1  X  1  0  X  1 X+1  1 X+1 X+1  X  1  1 X+1  1 X+1  X  1 X+1  0  X  1  1  0 X+1  1 X+1 X+1  0  1  1  1  0  1  X  1 X+1  X  X  1  X  0  1  1  1 X+1  1  1  X  1  1  1  1 X+1  0  0
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  X  0  0  0  X  0  0  X  0  X  X  X  X  0  0  X  X  X  X  X  0  0  X  0  0  0  0  0  X  X  0  X  0  0  X  0  0  X  X  X  X  X  0  0  0  X  X  X  0  X  0  0  0  X  0  X  0  X  0  0  0  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  0  X  X  X  0  X  X  X  X  0  0  0  X  0  0  X  X  0  0  X  X  X  0  X  0  0  X  X  X  X  0  X  0  0  0  X  X  0  X  0  X  0  0  X  0  X  0  0  X  0  X  0  X  X  0  X  X  0  0  X  X  0  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  0  X  X  0  0  0  X  X  X  X  0  X  0  X  0  X  0  X  X  X  0  0  X  0  X  X  0  0  0  X  0  0  X  0  X  0  X  0  X  X  0  0  X  X  0  X  X  X  X  0  X  0  0  X  X  X  X  X  X  0  0  0  X  0  0  0  0  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  X  X  X  0  X  X  X  X  0  X  X  0  X  X  0  X  0  X  0  X  X  0  X  0  X  X  0  X  0  X  0  X  0  X  X  X  0  0  0  0  0  X  0  X  X  X  0  X  0  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  0  X  0  0  X  X  0  X  0  X  X  0  X  0  0  0  0  X  0  X  0  X  X  X  0  X  0  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  X  0  X  X  X  X  X  X  X  X  X  0  0  X  X  0  0  0  0  X  0  0  0  X
 0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  X  X  0  X  0  X  X  X  0  0  X  0  X  0  X  X  X  0  X  0  X  0  0  0  X  X  0  0  0  0  X  X  0  0  X  0  0  0  X  X  X  0  X  X  0  0  0  X  X  0  0  X  X  0  0  0  X  X  X  X  X  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  0  X  X  X  X  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  0  0  X  X  0  X  0  X  X  0  0  X  X  X  0  X  X  0  X  0  0  0  X  0  X  0  X  0  0  X  X  X  X  X  0  X  X  0  X  0  X  X  X  X
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  X  X  0  X  X  0  X  X  0  0  X  X  0  X  0  0  0  X  X  0  X  X  X  X  0  X  0  0  X  0  X  0  0  X  X  0  0  0  0  0  0  X  X  X  X  X  X  0  X  0  X  0  0  X  0  0  X  0  X  0  X  X  0  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+40x^70+14x^71+84x^72+72x^73+145x^74+132x^75+175x^76+198x^77+210x^78+238x^79+234x^80+218x^81+196x^82+280x^83+202x^84+284x^85+179x^86+202x^87+163x^88+188x^89+138x^90+132x^91+107x^92+62x^93+71x^94+26x^95+24x^96+2x^97+28x^98+25x^100+9x^102+5x^104+5x^106+2x^108+3x^110+1x^112+1x^116

The gray image is a linear code over GF(2) with n=166, k=12 and d=70.
This code was found by Heurico 1.16 in 4.35 seconds.