  In the last years, a new family of energy density functionals directly
inspired by effective field theory (EFT) has been developed, among which the
ELYO (extended Lee-Yang Orsay) functional. In this paper, a new extension of
ELYO that includes the recently calculated fourth-order EFT terms is presented.
Compared to the previous version, the description of neutron-drop energies
slightly degrades for a harmonic trap $\hbar\omega =10$ MeV -- yet remaining
reasonable -- , but improves for $\hbar\omega =5$ MeV. Furthermore, the
obtained neutron effective mass agrees significantly better with
\textit{ab-initio} estimates.
