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

generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+34x^67+134x^68+224x^69+364x^70+462x^71+643x^72+768x^73+862x^74+972x^75+1151x^76+1376x^77+1412x^78+1514x^79+1664x^80+1832x^81+1797x^82+2028x^83+1897x^84+1800x^85+1974x^86+1666x^87+1571x^88+1338x^89+1104x^90+988x^91+768x^92+640x^93+530x^94+406x^95+299x^96+172x^97+117x^98+106x^99+55x^100+40x^101+30x^102+16x^103+5x^104+2x^105+3x^108+2x^110+1x^120

The gray image is a linear code over GF(2) with n=166, k=15 and d=67.
This code was found by Heurico 1.11 in 73.3 seconds.