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.