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

generates a code of length 59 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+32x^52+94x^53+78x^54+90x^55+100x^56+86x^57+84x^58+46x^59+56x^60+72x^61+53x^62+24x^63+41x^64+44x^65+27x^66+18x^67+20x^68+18x^69+5x^70+12x^71+6x^72+6x^73+9x^74+2x^79

The gray image is a linear code over GF(2) with n=118, k=10 and d=52.
This code was found by Heurico 1.10 in 0.062 seconds.