The generator matrix

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

generates a code of length 94 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+75x^78+146x^79+280x^80+432x^81+504x^82+700x^83+824x^84+950x^85+1056x^86+1234x^87+1360x^88+1436x^89+1615x^90+1548x^91+1583x^92+1664x^93+1757x^94+1698x^95+1727x^96+1722x^97+1553x^98+1566x^99+1312x^100+1214x^101+1170x^102+886x^103+686x^104+584x^105+469x^106+352x^107+231x^108+172x^109+110x^110+52x^111+57x^112+18x^113+11x^114+10x^115+2x^116+1x^160

The gray image is a linear code over GF(2) with n=188, k=15 and d=78.
This code was found by Heurico 1.11 in 86 seconds.