The generator matrix

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

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+30x^48+80x^49+102x^50+96x^51+80x^52+90x^53+75x^54+58x^55+56x^56+42x^57+56x^58+60x^59+32x^60+24x^61+42x^62+34x^63+17x^64+18x^65+10x^66+8x^67+8x^68+2x^69+3x^70

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 0.126 seconds.