The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+39x^48+60x^49+89x^50+118x^51+87x^52+84x^53+70x^54+60x^55+59x^56+64x^57+56x^58+36x^59+43x^60+36x^61+24x^62+28x^63+17x^64+12x^65+13x^66+14x^67+10x^68+2x^70+2x^74

The gray image is a linear code over GF(2) with n=110, k=10 and d=48.
This code was found by Heurico 1.10 in 0.063 seconds.