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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+76x^67+153x^68+218x^69+302x^70+310x^71+357x^72+416x^73+365x^74+420x^75+415x^76+444x^77+455x^78+416x^79+515x^80+464x^81+401x^82+410x^83+405x^84+294x^85+268x^86+276x^87+247x^88+162x^89+103x^90+126x^91+74x^92+42x^93+23x^94+14x^95+8x^96+6x^97+3x^98+2x^101+1x^108

The gray image is a linear code over GF(2) with n=158, k=13 and d=67.
This code was found by Heurico 1.10 in 3.98 seconds.