The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 X 1 1 1 1 1 1 X X 1 1 X 1 X X 1 1 X 1 1 0 0 X X 1
0 X 0 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 0 0 X X X X 0 X X 0 X X X X 0 X 0 0 0 X 0 X 0 0 0 X 0 0 0 X X X X X 0 X 0 X 0 X X 0
0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 0 0 X X 0 0 0 0 0 0 X X 0 0 X X X 0 X 0 X X X 0 0 X 0 X X X X 0 0 0 0 0 0 0 0 X X X 0
0 0 0 X 0 0 0 0 0 0 X 0 X X 0 X X 0 X 0 X X X X 0 X 0 X 0 0 X X 0 X X X X 0 0 X 0 0 0 0 X X 0 X 0 X 0 X 0 0 X X X 0 X 0
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 0 0 0 X X 0 X X X 0 0 X 0 X X 0 X 0 0 0 X 0 0 X 0 0 0 0 X X X X X X 0 X X 0
0 0 0 0 0 X 0 0 0 X 0 0 0 X X 0 X 0 X X X 0 0 X 0 X X X X X 0 X X X X 0 X X 0 X 0 X 0 0 0 X X 0 0 X X X X 0 X 0 0 0 0 0
0 0 0 0 0 0 X 0 0 X 0 0 X 0 0 X X X 0 X X 0 X X 0 0 X 0 0 0 X 0 X X X 0 0 X 0 X X 0 X 0 0 X 0 X 0 0 X X X 0 0 X X X X X
0 0 0 0 0 0 0 X 0 X X X X 0 0 0 0 0 X X X X X 0 X X 0 X X X 0 0 0 0 0 0 X X 0 X 0 X X 0 X 0 X 0 X X X 0 0 X 0 X 0 0 0 0
0 0 0 0 0 0 0 0 X X X X 0 0 X X X 0 0 0 X 0 0 0 X 0 X 0 0 X 0 0 X X 0 X 0 0 0 0 X 0 0 X X X X X 0 X X X 0 X X 0 0 0 0 X
generates a code of length 60 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.
Homogenous weight enumerator: w(x)=1x^0+32x^50+69x^52+18x^53+67x^54+52x^55+45x^56+92x^57+42x^58+100x^59+44x^60+96x^61+46x^62+92x^63+39x^64+36x^65+24x^66+12x^67+25x^68+14x^69+25x^70+25x^72+14x^74+6x^76+5x^78+2x^80+1x^94
The gray image is a linear code over GF(2) with n=120, k=10 and d=50.
This code was found by Heurico 1.16 in 0.244 seconds.