The generator matrix

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

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+23x^48+72x^49+87x^50+112x^51+100x^52+80x^53+78x^54+62x^55+68x^56+62x^57+50x^58+46x^59+34x^60+26x^61+26x^62+14x^63+28x^64+10x^65+13x^66+18x^67+2x^68+6x^69+4x^71+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 1.16 in 0.157 seconds.