The generator matrix
1 0 0 0 1 1 1 0 1 1 X 1 1 0 0 X X 1 0 1 1 0 1 X 1 X 1 X X 1 1 0 1 X X 1 1 1 1 0 0 0 1 1 X 1 0 1 1 1 1 1 0 1 1 X 1 1 1 1 X 0 0 1 1
0 1 0 0 0 1 1 1 X+1 X 1 0 1 1 X 1 1 1 1 X+1 0 0 0 X X+1 X X 1 1 X+1 X+1 1 1 0 0 0 X+1 X+1 0 1 1 1 1 1 1 0 1 1 X+1 X+1 1 1 1 0 X X X X+1 0 0 1 1 1 1 0
0 0 1 0 1 1 0 1 1 1 0 X X 1 1 0 0 1 X+1 X 0 1 X 1 0 1 1 0 X+1 X+1 X 1 1 X 1 X+1 X 1 0 0 X+1 X+1 X 0 1 X+1 0 1 X X+1 X X+1 1 X+1 0 1 0 1 0 1 X X X 1 0
0 0 0 1 1 0 1 X+1 X+1 0 X+1 1 X X 1 X+1 X 0 1 X+1 X X 1 1 X X X X 0 X+1 X+1 X 1 1 1 X+1 0 X 0 0 0 X+1 X+1 X+1 X+1 1 1 1 0 X+1 X+1 0 0 X+1 1 X+1 0 1 0 X+1 1 X 0 0 0
0 0 0 0 X 0 0 X X X 0 0 X 0 0 X X 0 X X X X 0 0 X 0 X 0 X 0 0 0 X X 0 X 0 X 0 X 0 X X X 0 0 X X 0 0 X X X 0 0 X 0 0 0 X 0 0 0 X X
0 0 0 0 0 X 0 0 0 0 0 0 X X X X X X 0 X X X X 0 0 0 X X X 0 X 0 0 0 0 X 0 X X 0 X X 0 X X 0 0 X X 0 0 X 0 X 0 0 0 X X 0 0 0 0 0 X
0 0 0 0 0 0 X 0 0 X X X X X 0 0 X X X 0 0 X 0 0 X X 0 0 X X 0 X X X X X X X X X 0 0 X X 0 0 0 0 X 0 0 0 0 0 0 X X 0 0 0 X X X X 0
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+36x^56+66x^57+92x^58+140x^59+173x^60+150x^61+134x^62+160x^63+132x^64+126x^65+89x^66+82x^67+120x^68+90x^69+68x^70+78x^71+80x^72+64x^73+42x^74+34x^75+27x^76+16x^77+22x^78+18x^79+7x^80+1x^82
The gray image is a linear code over GF(2) with n=130, k=11 and d=56.
This code was found by Heurico 1.16 in 0.593 seconds.