The generator matrix

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

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+45x^74+44x^75+147x^76+152x^77+221x^78+218x^79+251x^80+306x^81+423x^82+430x^83+419x^84+442x^85+403x^86+436x^87+436x^88+498x^89+407x^90+482x^91+339x^92+364x^93+296x^94+306x^95+271x^96+230x^97+158x^98+114x^99+125x^100+50x^101+63x^102+16x^103+44x^104+6x^105+22x^106+2x^107+10x^108+9x^110+5x^112+1x^114

The gray image is a linear code over GF(2) with n=176, k=13 and d=74.
This code was found by Heurico 1.16 in 16.2 seconds.