The generator matrix

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

generates a code of length 60 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+21x^56+46x^57+43x^58+34x^59+24x^60+28x^61+12x^62+8x^63+13x^64+4x^65+2x^66+2x^67+2x^68+4x^70+1x^72+2x^73+3x^74+4x^75+2x^76

The gray image is a linear code over GF(2) with n=120, k=8 and d=56.
This code was found by Heurico 1.10 in 0 seconds.