The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+62x^76+94x^77+173x^78+206x^79+276x^80+370x^81+368x^82+362x^83+369x^84+486x^85+426x^86+350x^87+426x^88+488x^89+407x^90+366x^91+411x^92+414x^93+356x^94+278x^95+297x^96+294x^97+244x^98+178x^99+147x^100+126x^101+47x^102+46x^103+38x^104+32x^105+19x^106+6x^107+19x^108+5x^110+2x^112+2x^114+1x^118

The gray image is a linear code over GF(2) with n=178, k=13 and d=76.
This code was found by Heurico 1.16 in 15.4 seconds.