The generator matrix
1 0 0 0 1 1 1 X 0 0 0 1 1 1 1 1 X 0 1 X 1 0 1 1 0 1 X 1 0 1 X 1 1 X 1 X 1 1 0 0 1 X 1 X 1 1 0 1 1 1 0 1 1 0 1 0 X X 0 1 1 1 1 1 1 1 1 X 0 X X 0 1 1 X 1 X X 0 0 X 0 1 X 1 0 0
0 1 0 0 0 0 0 0 1 1 1 1 X+1 1 1 X 1 X X+1 1 1 0 0 0 X X 1 1 1 X 1 1 X 1 0 X 0 1 1 X X+1 0 1 1 X X+1 X 0 1 X 0 X+1 0 1 1 1 0 1 1 0 0 X X 1 X+1 0 X 1 X 1 1 0 X+1 0 0 X+1 1 1 1 X 1 1 X 1 X+1 1 0
0 0 1 0 0 1 1 1 X 1 X+1 1 1 X 0 X+1 X 0 X+1 1 0 1 1 X 1 0 0 X 1 X+1 X+1 1 1 1 X 1 X 1 X 1 X+1 0 X 0 0 1 0 1 X+1 X+1 1 1 1 1 0 0 1 X 0 X X X+1 X+1 1 X X+1 X+1 1 1 X+1 X X X+1 0 1 X+1 1 X 1 0 X 1 X 1 X+1 1 X
0 0 0 1 1 1 0 1 1 X+1 X 0 1 X+1 X X 1 1 X X 1 0 X+1 X+1 X+1 X+1 X X 1 1 0 X+1 X X+1 0 1 X 0 1 0 1 1 0 X+1 1 X 1 1 1 X X X 0 0 0 X X+1 1 X 0 X X X X+1 0 1 1 0 X+1 X 1 1 1 0 X 1 1 0 1 1 X X+1 X+1 1 X X X
0 0 0 0 X 0 0 0 0 0 0 X X X X X X X 0 X 0 X X X 0 0 X 0 X X 0 X 0 0 0 0 0 X 0 0 X 0 0 X X 0 0 X X X X X X X X X X X X 0 0 X 0 0 0 0 0 0 X X X 0 0 X 0 0 0 0 0 0 0 X X X 0 0 X
0 0 0 0 0 X 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 0 X X 0 X 0 X 0 0 X X 0 X X X X 0 0 0 0 X X X 0 X 0 0 X X 0 0 0 X 0 X 0 X X X 0 X 0 X X X 0 X 0 0 0 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 0 X X X X X X X X X X X X X X X X X X X X X 0 X X X X X X X X 0 X X 0 X X 0 0 X X X X 0 X 0 0 X X 0 X 0 X
generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.
Homogenous weight enumerator: w(x)=1x^0+116x^78+215x^80+330x^82+275x^84+236x^86+188x^88+184x^90+126x^92+120x^94+84x^96+58x^98+45x^100+32x^102+24x^104+12x^106+2x^108
The gray image is a linear code over GF(2) with n=174, k=11 and d=78.
This code was found by Heurico 1.16 in 0.92 seconds.