The generator matrix

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

generates a code of length 91 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+66x^78+94x^79+172x^80+252x^81+311x^82+344x^83+345x^84+336x^85+429x^86+446x^87+336x^88+408x^89+442x^90+434x^91+383x^92+422x^93+428x^94+388x^95+345x^96+336x^97+284x^98+214x^99+236x^100+230x^101+149x^102+104x^103+80x^104+50x^105+54x^106+24x^107+19x^108+12x^109+8x^110+2x^112+2x^113+5x^114+1x^116

The gray image is a linear code over GF(2) with n=182, k=13 and d=78.
This code was found by Heurico 1.16 in 15.3 seconds.