The generator matrix

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

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+56x^67+144x^68+314x^69+487x^70+758x^71+884x^72+1044x^73+1426x^74+1608x^75+1862x^76+2220x^77+2597x^78+2956x^79+3261x^80+3520x^81+3584x^82+3714x^83+3980x^84+4018x^85+3822x^86+3570x^87+3394x^88+2972x^89+2789x^90+2440x^91+1888x^92+1634x^93+1240x^94+1000x^95+743x^96+536x^97+362x^98+228x^99+180x^100+100x^101+63x^102+52x^103+43x^104+24x^105+7x^106+2x^108+2x^109+7x^110+1x^112+2x^115+1x^120

The gray image is a linear code over GF(2) with n=168, k=16 and d=67.
This code was found by Heurico 1.11 in 288 seconds.