The generator matrix

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

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+77x^56+154x^57+260x^58+338x^59+481x^60+538x^61+626x^62+706x^63+720x^64+870x^65+909x^66+964x^67+1067x^68+1044x^69+980x^70+984x^71+926x^72+932x^73+774x^74+674x^75+556x^76+492x^77+433x^78+302x^79+238x^80+124x^81+107x^82+64x^83+28x^84+6x^85+5x^86+2x^88+1x^90+1x^114

The gray image is a linear code over GF(2) with n=138, k=14 and d=56.
This code was found by Heurico 1.10 in 12.4 seconds.