The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+64x^70+174x^72+256x^74+88x^75+266x^76+252x^77+406x^78+348x^79+489x^80+542x^81+549x^82+700x^83+634x^84+732x^85+599x^86+910x^87+686x^88+994x^89+616x^90+978x^91+640x^92+860x^93+594x^94+606x^95+557x^96+486x^97+533x^98+364x^99+370x^100+184x^101+321x^102+86x^103+192x^104+42x^105+122x^106+14x^107+70x^108+4x^109+30x^110+2x^111+13x^112+4x^114+4x^116+2x^118

The gray image is a linear code over GF(2) with n=178, k=14 and d=70.
This code was found by Heurico 1.16 in 99.9 seconds.