The generator matrix

 1  0  0  0  0  1  1  1  1  0  X  1  X  1  X  0  0  X  0  1  1  X  1  X  1  1  1  1  0  1  1  1  X  1  1  0  X  0  X  1  1  X  1  0  0  X  1  1  0  1  1  1  1  0  X
 0  1  0  0  0  0  0  0  X  0  0  X  X  0  1  1  1  1  1  1 X+1  1  1  1 X+1  1 X+1  X  0  X  1  1  1 X+1  0  1  1  1  1  X  X  0  0  1  X  0 X+1  0  X  X  0  0  X  0  X
 0  0  1  0  0  0  0  1  1  1  X X+1  1  X  1  0  X  1  1  0  0 X+1 X+1  0  1  X  1 X+1  1  1  0  X  0  X  0  1  1  1 X+1  0  X  1  1  X  1  1  1  X  0  X  X  X  X  1  X
 0  0  0  1  0  1  X  X  0  X  1 X+1  1 X+1  0  1  0 X+1  1  X X+1  X  1  1 X+1  X  0 X+1  1  X  0 X+1 X+1 X+1  0  1  X X+1 X+1  1  1  0  X  0  X X+1  1  0  X X+1  X  0 X+1  1  0
 0  0  0  0  1  1  1 X+1  0  1 X+1  X  1  X  X  X X+1  0  1  0  0  1  1 X+1  X  1 X+1 X+1  X X+1  X  X  0  1 X+1  1  X X+1  X X+1  0  0  0 X+1  X  X  1 X+1  1  0  1  X  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  X  X  X  X  0  X  0  X  X  0  X  X  X  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+303x^48+146x^50+473x^52+130x^54+352x^56+112x^58+258x^60+88x^62+126x^64+30x^66+21x^68+6x^70+2x^72

The gray image is a linear code over GF(2) with n=110, k=11 and d=48.
This code was found by Heurico 1.16 in 77.6 seconds.