The generator matrix

1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 X 0 X 1 1 1 1 1 0 1 1 0 1 0 0 1 1 X 1 X 1 X X 0 0 X 1 X X 1 0 1 1 1 1 1 1 0 0 1 X X 1 0 0 0 1 1 1 1 0 1 X 0 1 1 X 1 0 X 1 X X 0 1 1 1 X 1 X X 1
0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X X+1 X 1 1 1 0 1 X+1 X+1 0 X+1 X+1 1 1 1 1 X 0 1 X+1 1 X 1 0 1 1 X X 0 1 0 1 X X+1 1 1 1 X 0 1 X X X X 1 0 1 X X+1 0 X 1 0 0 1 1 X 0 X X 1 1 0 0 1 X 0 X 1 X+1 X 1 0
0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 1 1 1 1 X 1 X+1 0 X X 1 0 1 1 0 X 0 X+1 X 1 X 1 0 X+1 1 X+1 0 0 X X X+1 X X+1 1 1 X 0 1 X+1 1 0 X+1 1 1 1 1 1 0 X X+1 1 1 1 X+1 1 X X 1 1 1 1 0 0 0 1 X X X+1 1 X X+1 X X+1 0
0 0 0 1 0 0 0 1 1 1 1 1 0 1 X X+1 0 1 X 0 X 1 X 1 X+1 X 0 X+1 X+1 X+1 1 0 X X+1 0 1 X+1 1 0 X X+1 1 1 X 1 X+1 1 0 0 X 0 X X+1 1 X+1 1 1 X X 1 1 X+1 1 X+1 X 0 1 0 0 X+1 1 1 1 1 X+1 X+1 X+1 0 0 X+1 X+1 0 X 0 1 0 1 1 0
0 0 0 0 1 0 1 0 X+1 1 1 1 X X+1 1 X 1 X X+1 1 0 X+1 X+1 0 X+1 X+1 X 0 X 1 X 0 0 1 1 X X+1 0 X 0 X 1 X 1 X+1 0 X X X+1 X X 1 X X+1 0 X X X+1 1 1 X X+1 0 X 1 X+1 X X+1 X 1 0 0 X+1 X+1 X X+1 X+1 X+1 X X 1 1 X+1 X 1 0 1 X+1 0
0 0 0 0 0 1 1 X+1 X 1 0 X 1 X+1 X 0 X+1 X+1 0 X+1 0 1 X 0 1 X+1 X+1 X+1 X X+1 1 0 X+1 0 0 X 1 1 X+1 X+1 1 X+1 1 X X X+1 0 X 1 1 0 1 X 0 X 0 X+1 X X X+1 0 1 X+1 0 X+1 X 1 1 X 0 X+1 X+1 X X+1 0 X+1 1 X 1 1 0 X X X 0 X 1 1 0
0 0 0 0 0 0 X X 0 0 0 0 0 0 X X X 0 0 0 X X X X X 0 X 0 X 0 X X 0 X X 0 X 0 X X X X X X X 0 X X 0 0 0 X 0 0 0 0 X X 0 0 X X 0 0 0 0 0 0 0 X X 0 X 0 0 0 0 0 0 X X X X 0 X 0 X 0 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+52x^76+88x^77+175x^78+266x^79+294x^80+334x^81+378x^82+380x^83+415x^84+412x^85+393x^86+420x^87+393x^88+418x^89+368x^90+398x^91+413x^92+392x^93+386x^94+340x^95+282x^96+268x^97+244x^98+166x^99+136x^100+102x^101+86x^102+66x^103+50x^104+28x^105+13x^106+8x^107+12x^108+6x^109+4x^110+4x^111+1x^114

The gray image is a linear code over GF(2) with n=178, k=13 and d=76.
This code was found by Heurico 1.10 in 4.47 seconds.