The generator matrix
1 0 0 0 1 1 1 X 1 1 X X 1 1 0 1 0 1 1 1 1 1 1 1 X 0 X 0 1 0 0 X 1 1 X 1 0 1 1 0 1 X 0 1 X X 0 1 0 X 1 X 1 0 1 1 1 1 0 1 1 1 1 0 1 X X 1
0 1 0 0 0 0 0 X 1 X+1 1 1 X+1 X+1 1 0 X 1 0 1 X 1 X+1 X 1 1 1 1 0 1 0 X X+1 X X 0 X X 1 1 X+1 0 1 0 1 1 0 1 1 1 X 1 X X X+1 X+1 1 0 0 0 0 1 0 X X+1 1 1 0
0 0 1 0 0 1 X+1 1 X+1 1 X 1 0 X X+1 X 1 1 X+1 X 1 X+1 0 X 1 X X+1 0 X 0 1 1 X X+1 1 0 X X+1 1 0 0 1 1 1 0 0 X 1 X+1 1 0 0 1 0 0 0 X X+1 1 X X+1 1 X 0 X X 0 0
0 0 0 1 1 1 0 1 X X+1 X+1 0 0 1 1 0 0 X X 1 X+1 X+1 0 X+1 X 0 X+1 X+1 X X X+1 X X+1 0 0 X+1 1 1 X X X X+1 1 X+1 0 X+1 1 0 X X X+1 X+1 0 1 1 0 0 X+1 X+1 1 0 X+1 1 1 0 X X X
0 0 0 0 X 0 0 X 0 0 0 X X X X X X X X 0 X X 0 0 0 0 0 0 X X X X 0 0 0 X X X 0 X 0 0 0 0 0 0 X X X 0 X X X 0 X 0 0 X 0 0 0 X X X X 0 X 0
0 0 0 0 0 X X X X X 0 X 0 0 X 0 X 0 0 X 0 0 X X X X X X X 0 0 0 0 0 X X 0 X 0 X 0 X 0 0 X 0 X X 0 0 X 0 0 0 X 0 X X 0 0 0 X X 0 0 0 X 0
generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 61.
Homogenous weight enumerator: w(x)=1x^0+56x^61+85x^62+78x^63+100x^64+100x^65+82x^66+58x^67+64x^68+66x^69+31x^70+38x^71+53x^72+36x^73+35x^74+32x^75+23x^76+18x^77+14x^78+12x^79+10x^80+12x^81+7x^82+2x^83+5x^84+2x^86+4x^87
The gray image is a linear code over GF(2) with n=136, k=10 and d=61.
This code was found by Heurico 1.16 in 0.192 seconds.