The generator matrix

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

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+103x^44+116x^45+181x^46+254x^47+345x^48+340x^49+391x^50+484x^51+472x^52+560x^53+552x^54+564x^55+547x^56+584x^57+544x^58+512x^59+420x^60+340x^61+253x^62+222x^63+126x^64+100x^65+103x^66+12x^67+28x^68+8x^69+22x^70+5x^72+2x^74+1x^76

The gray image is a linear code over GF(2) with n=110, k=13 and d=44.
This code was found by Heurico 1.16 in 7.88 seconds.