The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  1  X  1  1  1  0  1  1  X  1  1  1  1  1  1  X  1  X  1  0  X  X  X  1  1  1  0  X  0  0  X  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  X  0  X  X  0  0  X  0  0  X  X  0  X  X  X  0  0  0  0  X  X  0  0  X  X  X  0  0  0  X  X  X  X  X  X  0  0  X  0  0  0  0  0  X  X  X  X  X  0  X  0  X  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  0  0  X  0  0  X  X  X  X  0  0  0  0  0  X  X  0  X  0  0  0  X  X  0  0  0  X  X  X  X  0  0  X  0  X  0  X  X  X  0  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  X  0  0  X  X  X  X  X  X  0  X  0  X  X  0  X  0  0  X  0  0  0  0  0  X  0  X  X  0  X  0  0  0  X  X  0  0  X  0  0  0  X  0  X  0  0  0  X  0  X  X  0  X  0  X  X  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  0  X  0  X  0  0  X  0  X  0  0  0  0  0  X  X  0  0  X  X  X  0  X  0  X  X  0  X  X  X  X  0  X  X  0  0  0  0  0  X  X  0  X  X  0  0  X  0  0  0  X  0  X  0  0  X  X  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  X  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  X  X  X  0  X  X  X  0  X  0  0  X  X  0  X  0  X  X  0  0  X  0  X  X  0  0  0  X  0  0  X  0  0  X  0  X  0  X  0  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  0  X  X  X  0  X  X  X  0  0  0  0  X  X  0  X  0  X  X  X  X  0  X  X  X  X  0  0  0  X  X  0  0  0  0  0  X  0  0  0  0  X  0  X  0  X  X  0  X  X  0  X  X  X  X  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  X  0  X  0  X  X  X  0  X  X  0  X  0  0  X  0  X  0  0  X  X  0  X  0  0  X  X  X  X  X  X  X  0  X  X  0  X  X  0  X  X  X  X  0  X  0  X  0  X  0  0  X  X  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  0  0  X  X  0  0  X  X  0  X  0  X  0  0  X  0  0  X  X  X  X  0  0  X  0  0  0  0  X  0  X  X  X  0  X  0  0  X  0  X  X  0  0  X  0  X  X  X  0  0  X  0  0  X  X  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  X  X  X  0  X  0  X  X  X  0  X  0  X  0  X  0  0  X  0  X  0  0  0  0  0  X  X  0  X  X  X  X  0  X  X  0  0  X  X  X  X  0  0  X  X  0  X  X  X  0  X  0  0  X  X  0  0  X  X  0

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+49x^68+42x^70+4x^71+84x^72+28x^73+71x^74+82x^75+107x^76+108x^77+82x^78+114x^79+81x^80+168x^81+71x^82+180x^83+65x^84+136x^85+76x^86+104x^87+49x^88+60x^89+69x^90+26x^91+41x^92+12x^93+50x^94+2x^95+22x^96+24x^98+10x^100+22x^102+3x^104+3x^106+1x^114+1x^122

The gray image is a linear code over GF(2) with n=164, k=11 and d=68.
This code was found by Heurico 1.16 in 1.37 seconds.