The generator matrix

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

generates a code of length 61 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+40x^54+84x^55+95x^56+94x^57+93x^58+102x^59+65x^60+52x^61+40x^62+38x^63+51x^64+46x^65+45x^66+30x^67+31x^68+36x^69+30x^70+14x^71+11x^72+8x^73+8x^74+4x^75+2x^76+4x^77

The gray image is a linear code over GF(2) with n=122, k=10 and d=54.
This code was found by Heurico 1.10 in 0.062 seconds.