The generator matrix
1 0 0 0 1 1 1 X 0 1 1 1 1 0 X X 1 0 1 1 1 1 X 0 X 0 0 1 1 1 1 X 1 X 1 1 X X 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1
0 1 0 0 0 0 0 0 1 1 X+1 1 X+1 1 1 1 0 X X+1 1 X 0 1 X 1 0 1 0 X 1 X X 1 X 0 X 1 1 0 X+1 X 1 1 0 1 1 X 1 X 0 0 X X 0 1
0 0 1 0 0 1 1 1 X X+1 X+1 X X 1 1 X X 0 0 1 X+1 X X+1 0 0 1 X+1 X+1 X X+1 X+1 1 1 X X 0 X X X X X X+1 X 1 X X+1 1 X X+1 1 X+1 1 0 0 0
0 0 0 1 1 1 0 1 1 X X+1 X+1 0 X+1 X X+1 X+1 1 X 1 X X 0 1 X 0 0 X+1 1 X X+1 1 X 1 1 X X+1 0 0 X 0 0 1 0 0 0 X+1 X X+1 0 0 0 1 1 X+1
0 0 0 0 X 0 0 0 0 0 X 0 0 X 0 X X X X X X X X 0 0 0 X 0 0 X 0 X X X 0 0 X 0 X 0 X 0 0 X X X 0 X X X X X X 0 X
0 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X X X X X 0 0 0 X X X X X 0 0 X 0 0 X X 0 0 X 0 0 0 X X 0 X 0 X 0 0 X X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 X 0 0 X 0 X 0 0 0 X X 0 X 0 X X X 0 0 X X X X X X 0 X 0 X 0 X 0 X X 0 0 X X X 0 X 0 X 0
generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 47.
Homogenous weight enumerator: w(x)=1x^0+66x^47+145x^48+122x^49+98x^50+142x^51+229x^52+146x^53+42x^54+126x^55+162x^56+142x^57+78x^58+94x^59+144x^60+70x^61+30x^62+72x^63+66x^64+32x^65+8x^66+12x^67+19x^68+2x^72
The gray image is a linear code over GF(2) with n=110, k=11 and d=47.
This code was found by Heurico 1.16 in 5.46 seconds.