The Ice Cube Neutrino Observatory has been measuring an isotropic astrophysical neutrino flux in multiple detection channels for almost a decade. Galactic diffuse emission, which arises from the interactions between cosmic rays and the interstellar medium, is an expected signal in IceCube. The superposition of an extragalactic flux and a galactic flux results in directional structure and variations in the spectrum. In this work, we use 12.3 years of high-purity muon-neutrino induced muon track data to perform a dedicated search for this galactic emission, combined with a spectral measurement of the isotropic astrophysical neutrino flux. To distinguish a galactic component from the dominant atmospheric and isotropic astrophysical components, the precise directional information available for muon tracks is fully utilized in a three-dimensional forward folding likelihood fit. We test a state-of-the-art model prediction of galactic diffuse emission based on recent cosmic ray data (CRINGE). We fit this prediction as a template scaled by a factor $\Psi_{\mathrm{CRINGE}}$, and find $2.9\pm 1.1 \times \Psi_{\mathrm{CRINGE}}$ with a significance of $2.7\sigma$ in an energy range between 400 GeV and 60 TeV in the Northern Sky.