The generator matrix

 1  0  0  0  0  0  1  1  1  X  0  0  0  0  1  1  1  X  X  0  1  1  1  1  0  1  X  1  1  1  X  0  1  X  X  0  X  1  1  0  X  X  1  X  0  1  1  1  1  0  1  X  0  0  0  1  1  X  X  0  X  1  1  1  1  X  0  1
 0  1  0  0  0  0  0  0  0  0  1  X  1  1  0  1  X  X  1  1  X  1  0  1  X  1  1  1  1 X+1  0  1  X  1  0  1  1  0 X+1  X  X  X  0  1  1  0  1  X  1  1  X  1  X  X  0  0  0  1  1  0  X X+1  0  0  X  0  0  0
 0  0  1  0  0  0  0  0  0  0  X  1  1 X+1 X+1 X+1  1  1  0  X  0  0 X+1 X+1  1  0  X  X X+1  X  1 X+1 X+1  1  1  0  X X+1  0  X  1  0 X+1  0  1  0  0 X+1  X  X X+1  X  X  0  1  1  1  1  0  X  1 X+1  X X+1 X+1  0  1  0
 0  0  0  1  0  0  0  1  1  1 X+1 X+1  1  X  0 X+1  1  1  0  1 X+1  X  1  X  X  1  1  0  0  X  1  X  0 X+1 X+1  1  X  X  1  1 X+1  X X+1  1  X  X  1  1  X  0  1  0  X  1  1  X  1  0 X+1  1  X X+1 X+1  0  1  1  0  0
 0  0  0  0  1  0  1  1  X X+1  1  1  1  0 X+1  0  X  X X+1  X X+1 X+1  1  X  1  X  0  0 X+1  0  0  0  X X+1  1 X+1  1  X X+1  0  1  1  1  X  X  0  0 X+1 X+1  1  0  0  1 X+1  X  1  1  0  X  1  0  0 X+1  1 X+1 X+1  X  0
 0  0  0  0  0  1  1  X X+1  1  0  X  1 X+1  0 X+1  0  1 X+1 X+1  X  0 X+1  X X+1  0 X+1  1  1 X+1  1 X+1  1 X+1  X  0  1  1 X+1  1 X+1  1  1  X  0 X+1 X+1  X  1  X X+1  0  1  X  X  1  0  X  X  0  X  0  X  X  1  X  0  0
 0  0  0  0  0  0  X  0  X  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  X  0  X  0  0  X  X  X  X  X  X  X  X  0  X  X  X  X  0  X  X  X  0  X  0  X  0  0  0  X  0  0  0  X  0  X  X  0  X  X  0  0  0  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+80x^57+217x^58+234x^59+304x^60+386x^61+347x^62+436x^63+419x^64+494x^65+470x^66+482x^67+480x^68+472x^69+469x^70+436x^71+439x^72+382x^73+343x^74+328x^75+262x^76+188x^77+164x^78+110x^79+72x^80+44x^81+34x^82+20x^83+10x^84+2x^85+3x^86+2x^87+1x^88+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 1.16 in 10.1 seconds.