The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  X  1  1  1  1  0  1  X  1  1  1  0  1  1  0  1  X  1  0  1  1  1  1  X  1  1  1  1  X  1  0  1  X  1  1  1  0  0  1  1  X  X  1
 0  1  1  0  1  1  0  1  1  X X+1  1  1  0 X+1  0 X+1  1 X+1  1  X  0 X+1  1 X+1  0  1  0  1 X+1  1 X+1  0  0  X  1  X X+1 X+1  0  1  X  1  X  1  1 X+1  1  1  1 X+1  0  1  1  0
 0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  X  X  0  0  X  0  X  0  X  0  X  X  0  0  X  X  X  0  0  X  0  X  X  0  0  X
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  X  X  X  X  0  X  X  0  0  0  X  0  X  0  X  X  X  X  0  0  X  X  X  0  0  0  0  X  X  0  0  X  X  X
 0  0  0  0  X  0  0  0  0  0  X  X  X  X  0  X  X  X  X  X  0  X  X  X  0  X  0  X  X  0  X  X  X  X  X  0  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  0  X  X  0
 0  0  0  0  0  X  0  0  X  0  0  X  0  X  0  X  0  X  0  0  0  X  X  X  X  0  X  0  X  X  0  X  0  0  X  X  X  0  X  0  X  X  0  0  0  X  X  0  X  0  0  0  0  0  X
 0  0  0  0  0  0  X  0  X  X  0  0  X  X  0  0  X  0  X  0  X  X  X  X  0  0  0  0  X  X  X  0  X  X  0  X  0  0  X  0  0  X  X  0  0  X  0  X  0  0  X  0  X  X  X
 0  0  0  0  0  0  0  X  X  0  X  0  X  X  X  0  0  X  0  X  X  X  0  X  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  X  X  0  0  0  X  0  0  0  X  X  X  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+129x^48+98x^50+192x^52+98x^54+151x^56+118x^58+128x^60+70x^62+20x^64+6x^68+11x^72+2x^76

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 0.164 seconds.