The generator matrix

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

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+322x^44+790x^46+1231x^48+1570x^50+1886x^52+2312x^54+2377x^56+2074x^58+1682x^60+1144x^62+588x^64+280x^66+101x^68+18x^70+2x^72+4x^74+1x^84+1x^88

The gray image is a linear code over GF(2) with n=110, k=14 and d=44.
This code was found by Heurico 1.10 in 10.1 seconds.