The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+61x^44+114x^45+238x^46+284x^47+340x^48+382x^49+415x^50+452x^51+492x^52+556x^53+541x^54+566x^55+487x^56+514x^57+470x^58+482x^59+428x^60+368x^61+309x^62+226x^63+208x^64+104x^65+70x^66+34x^67+31x^68+10x^69+4x^70+4x^71+1x^90

The gray image is a linear code over GF(2) with n=110, k=13 and d=44.
This code was found by Heurico 1.10 in 2.47 seconds.