The generator matrix

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

generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+158x^68+216x^70+747x^72+702x^74+1325x^76+1372x^78+1859x^80+1754x^82+2035x^84+1600x^86+1710x^88+1058x^90+921x^92+380x^94+331x^96+70x^98+99x^100+16x^102+23x^104+6x^108+1x^112

The gray image is a linear code over GF(2) with n=166, k=14 and d=68.
This code was found by Heurico 1.16 in 57.5 seconds.