We report on the first results of the Noble and Alkali Spin Detectors for Ultralight Coherent darK matter (NASDUCK) collaboration. We search for the interactions of Axion-Like Particles (ALPs) with atomic spins using an earth-based precision quantum detector as it traverses through the galactic dark matter halo. The detector is composed of spin-polarized xenon gas which can coherently interact with a background ALP dark matter field and an in-situ rubidium Floquet optical-magnetometer. Conducting a five months-long search, we derive new constraints on ALP-proton and ALP-neutron interactions in the 4 × 10 −15 − 4 × 10 −12 eV/c 2 mass range. Our limits on the ALP-proton (ALP-neutron) couplings improve upon previous terrestrial bounds by up to 3 orders of magnitude for masses above 4 × 10 −14 eV/c 2 (4 × 10 −13 eV/c 2 ). Moreover, barring the uncertain supernova constraints, the ALP-proton bound improves on all existing terrestrial and astrophysical limits, partially closing the unexplored region for couplings in the range 10 −6 GeV −1 to 2 × 10 −5 GeV −1 . Finally, we also cast bounds on pseudo-scalar dark matter models in which dark matter is quadratically-coupled to the nucleons.