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 X 1 1 0 1 1 X 0 X 0 1 1 1 1 1 X 1 0 0 X 1 1 1 0 1 1 1 0 1 X 1 1 X 1 0 X X 1 0 0 X 1 0 1 1 1 0 1 X 0 1 X X 1 1 1
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 0 X 1 X 1 X+1 1 0 X 0 X 1 1 X 1 X X+1 X 1 0 0 1 1 1 1 X+1 X 1 X+1 1 0 0 X+1 0 X+1 X 1 X 1 1 0 0 1 1 X X+1 0 X+1 X+1 X 1 X+1 X 0 1 X X 1 X 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 1 X 0 1 X 1 X+1 1 1 1 0 0 X 1 X+1 X X+1 1 1 X+1 0 0 0 1 0 X 1 X+1 0 1 X+1 1 1 X+1 0 0 X+1 X+1 0 X X 1 0 1 1 X X+1 X+1 X 0 0 1 1 X 1 X+1 0 X+1
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 1 X+1 1 X X 1 X X 1 X X+1 X+1 0 1 1 X+1 X X X 0 X X X X 0 1 1 X+1 X X+1 1 1 X 0 0 X 1 0 1 X+1 1 X+1 0 X+1 1 X+1 X X X+1 X+1 X+1 X+1 1 X+1 X+1 1 0 0 0 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 X 0 0 X X X 0 0 X X X X 0 X 0 0 X X 0 0 0 0 0 X X X 0 X X X 0 0 X X 0 X X 0 0 X 0 X X X 0 0 0 0 X 0 0 0 X X X 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 X X X X X X X X X X 0 0 X 0 0 0 X 0 0 X X X 0 X 0 X 0 X 0 X X 0 0 X X X X X X X 0 X 0 0 X X 0 0 X 0 0 X X X X X 0 X 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 X X X X X X X X X X X X X X X X X X X X X X X 0 0 X X X 0 X 0 X X 0 0 0 X X X 0 X X X 0 X 0 X 0 X 0 X
generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 75.
Homogenous weight enumerator: w(x)=1x^0+52x^75+133x^76+118x^77+89x^78+152x^79+184x^80+138x^81+114x^82+112x^83+124x^84+106x^85+70x^86+90x^87+94x^88+82x^89+50x^90+52x^91+53x^92+44x^93+39x^94+32x^95+35x^96+20x^97+20x^98+16x^99+10x^100+4x^101+2x^102+6x^103+6x^104
The gray image is a linear code over GF(2) with n=168, k=11 and d=75.
This code was found by Heurico 1.16 in 0.89 seconds.