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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+60x^56+102x^57+191x^58+236x^59+302x^60+336x^61+374x^62+472x^63+458x^64+466x^65+461x^66+464x^67+472x^68+498x^69+436x^70+434x^71+442x^72+422x^73+371x^74+316x^75+230x^76+168x^77+171x^78+116x^79+71x^80+50x^81+39x^82+8x^83+12x^84+6x^85+2x^86+2x^87+2x^90+1x^94

The gray image is a linear code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.10 in 3.2 seconds.