The generator matrix

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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+25x^56+78x^57+124x^58+140x^59+138x^60+138x^61+140x^62+140x^63+146x^64+132x^65+89x^66+104x^67+94x^68+90x^69+104x^70+70x^71+61x^72+52x^73+42x^74+50x^75+40x^76+20x^77+12x^78+6x^79+7x^80+2x^81+1x^82+2x^83

The gray image is a linear code over GF(2) with n=130, k=11 and d=56.
This code was found by Heurico 1.10 in 0.203 seconds.