The generator matrix

 1  0  0  0  0  1  1  1  1  0  X  1  X  1  X  0  0  X  0  1  1  X  1  X  1  1  1  1  0  1  1  1  1  1  0  1  X  1  0  X  1  0  X  0  1  0  1  X  0  1  0  0  1  X  0  1  X  X  1  0  0  1  X  0  X  0  1  1  0  0  1  1  X  1  X  X  0
 0  1  0  0  0  0  0  0  X  0  0  X  X  0  1  1  1  1  1  1 X+1  1  1  1  1 X+1 X+1 X+1  X X+1  X  1 X+1  0  0  0  1  X  0  X  X  X  1  1  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  1  1  1  1  0  1 X+1  0  0  1
 0  0  1  0  0  0  0  1  1  1  X X+1  1  X  1  0  X  1  1  0  0 X+1 X+1  0  1  X X+1  0  1  1 X+1 X+1  0 X+1  1  0  X  1  1  0  X  1  1 X+1  1  X  1  0  X  1  1  X  1  X  X  X  0  1  X  X X+1 X+1  1  X  1  1  X  0  0  1  X  0  X  X  X  0  0
 0  0  0  1  0  1  X  X  0  X  1 X+1  1 X+1  0  1  0 X+1  1  X X+1  X  1  1  1  1  0  0  1  0 X+1  1  0 X+1  X  X  X  0  1  1 X+1  0 X+1 X+1  X  0  1  0  1  X  X  0 X+1  0  0 X+1  X X+1  1  1  1  1 X+1  X  0 X+1  1  X  1  0 X+1  1  1  0  1  1  0
 0  0  0  0  1  1  1 X+1  0  1 X+1  X  1  X  X  X X+1  0  1  0  0  1  1 X+1  X X+1  0 X+1  0 X+1 X+1  0  1  0  1  X X+1  0 X+1 X+1  X  X  1  X  X  1 X+1  1  X  0 X+1 X+1  X  1  1 X+1  1 X+1  0  0  0  0  0  1  X  1 X+1 X+1  0  X  X X+1  0 X+1  1  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  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  0  X  X  0  0  X  0  X  X  0  X  X  X  X  X  0  0  X  0  0  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+36x^68+80x^69+147x^70+152x^71+118x^72+162x^73+128x^74+134x^75+136x^76+106x^77+121x^78+98x^79+92x^80+74x^81+70x^82+78x^83+49x^84+58x^85+45x^86+34x^87+35x^88+16x^89+30x^90+12x^91+9x^92+12x^93+3x^94+4x^95+2x^96+4x^97+2x^100

The gray image is a linear code over GF(2) with n=154, k=11 and d=68.
This code was found by Heurico 1.16 in 0.715 seconds.