The generator matrix

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

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+49x^68+82x^69+255x^70+348x^71+538x^72+608x^73+759x^74+912x^75+1044x^76+1140x^77+1284x^78+1404x^79+1558x^80+1744x^81+1739x^82+1926x^83+1849x^84+1864x^85+1815x^86+1846x^87+1612x^88+1614x^89+1369x^90+1148x^91+1016x^92+766x^93+711x^94+494x^95+413x^96+302x^97+208x^98+100x^99+96x^100+60x^101+46x^102+12x^103+14x^104+12x^105+3x^106+2x^107+2x^108+1x^110+1x^114+1x^122

The gray image is a linear code over GF(2) with n=168, k=15 and d=68.
This code was found by Heurico 1.11 in 73 seconds.