I am a little confused about the units of the quadrupole moment. In the database, they are expressed in barns which is a unit of area. Where did the unit of charge go? Should it not be expressed in Coulomb x barns? I know it is probably a quite obvious answer but I am still a little confused.
If you look at the scientific paper that is provided as optional reading material, the second page gives an overview of what is given in the different columns of the table. There it is written that the units of the electric quadrupole moment are in eb (electron barn), which would resolve your question. I guess that the units in the table takes this implicitly into account?