The generator matrix
1 0 0 0 1 1 1 0 1 1 1 X 1 0 0 1 X 1 0 1 X 1 1 1 1 1 1 0 X 1 0 1 1 0 1 1 1 X X 1 1 0 1 X 1 1 X 1 1 0 1 0 1 X X 1 0 0 X 1 1
0 1 0 0 0 1 1 1 X+1 X 1 1 0 1 X 1 1 1 1 X 0 X+1 X+1 X 1 X X 0 1 X 0 X+1 0 1 X+1 0 X+1 0 1 X X 1 0 X 0 X 0 0 1 1 1 0 0 1 0 X 1 1 1 X+1 0
0 0 1 0 1 1 0 1 1 1 X 0 X 1 1 1 0 X 0 0 1 0 1 X+1 X X+1 1 1 X 0 1 X+1 1 X 0 X 1 1 X X+1 1 X+1 X 1 X X 1 X 1 X X X 0 0 1 1 1 1 1 1 0
0 0 0 1 1 0 1 X+1 X+1 0 X X+1 1 X 1 0 1 1 X X X X X+1 0 0 X+1 1 X+1 X+1 X 0 1 X X+1 0 X+1 1 1 0 1 X+1 0 X+1 1 X+1 X 1 0 X+1 X+1 1 1 X+1 X+1 0 X X+1 1 1 1 0
0 0 0 0 X 0 0 X X X X X 0 0 0 0 X 0 X 0 0 X 0 0 X X X 0 0 0 0 X X 0 0 X 0 X 0 0 0 X X 0 0 X X 0 0 X X X 0 X X X X 0 X 0 0
0 0 0 0 0 X 0 0 0 0 X X 0 X X X X 0 X 0 0 0 0 0 0 X X 0 X X X X X 0 X 0 X X 0 0 X 0 X 0 X 0 X X 0 0 X 0 X X 0 0 X 0 X 0 0
0 0 0 0 0 0 X 0 0 X X 0 X X 0 X X 0 X X X X 0 X 0 X 0 X X 0 0 X 0 0 X 0 0 X X 0 0 X 0 0 0 X 0 X 0 X X 0 X X 0 X 0 0 X 0 0
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+41x^52+70x^53+107x^54+138x^55+141x^56+140x^57+131x^58+138x^59+141x^60+130x^61+105x^62+108x^63+101x^64+96x^65+98x^66+88x^67+53x^68+62x^69+49x^70+34x^71+27x^72+12x^73+19x^74+6x^75+5x^76+2x^77+3x^78+2x^80
The gray image is a linear code over GF(2) with n=122, k=11 and d=52.
This code was found by Heurico 1.16 in 0.528 seconds.