I think the easiest way to visualise the various multipoles is through their connection with the spherical harmonics. These are probably best known as the functions that give the shape of the atomic orbitals in the hydrogen atom.
The $p$ orbitals correspond to a dipole, the $d$ orbitals to quadrupole and the $f$ orbitals to an octapole, that is a charge distribution of this shape creates a dipole/quadrupole/octapole. So a charge distribution creating a hexadecapole would look like the $g$ orbitals.
I've just spotted Hexadecapole potential using point particles?, which gives the same answer I've given so I suppose this question is a duplicate.