  We study complex algebraic K3 surfaces with finite automorphism groups and
polarized by rank-fourteen, 2-elementary lattices. Three such lattices exist,
namely $H \oplus E_8(-1) \oplus A_1(-1)^{\oplus 4}$, $H \oplus E_8(-1) \oplus
D_4(-1)$, and $H \oplus D_8(-1) \oplus D_4(-1)$. As part of our study, we
provide birational models for these surfaces as quartic projective
hypersurfaces and describe the associated coarse moduli spaces in terms of
suitable modular invariants. Additionally, we explore the connection between
these families and dual K3 families related via the Nikulin construction.
