The generator matrix

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

generates a code of length 61 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+207x^52+418x^54+489x^56+506x^58+538x^60+462x^62+465x^64+374x^66+287x^68+188x^70+109x^72+32x^74+16x^76+4x^78

The gray image is a linear code over GF(2) with n=122, k=12 and d=52.
This code was found by Heurico 1.10 in 1.13 seconds.