The generator matrix

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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+30x^68+74x^69+143x^70+160x^71+138x^72+154x^73+126x^74+144x^75+128x^76+110x^77+125x^78+88x^79+86x^80+86x^81+74x^82+68x^83+47x^84+52x^85+43x^86+36x^87+37x^88+20x^89+26x^90+12x^91+11x^92+12x^93+5x^94+4x^95+2x^96+4x^97+2x^98

The gray image is a linear code over GF(2) with n=154, k=11 and d=68.
This code was found by Heurico 1.10 in 0.25 seconds.