The generator matrix

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

generates a code of length 61 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+130x^50+477x^52+652x^54+900x^56+960x^58+1027x^60+990x^62+997x^64+808x^66+625x^68+366x^70+180x^72+62x^74+15x^76+1x^80+1x^96

The gray image is a linear code over GF(2) with n=122, k=13 and d=50.
This code was found by Heurico 1.10 in 2.83 seconds.