The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+45x^46+44x^47+101x^48+130x^49+120x^50+140x^51+142x^52+154x^53+132x^54+148x^55+109x^56+134x^57+120x^58+114x^59+100x^60+62x^61+75x^62+54x^63+52x^64+32x^65+14x^66+10x^67+4x^68+4x^70+2x^71+1x^72+2x^74+2x^76

The gray image is a linear code over GF(2) with n=110, k=11 and d=46.
This code was found by Heurico 1.16 in 0.499 seconds.