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The subsequent observing runs of the advanced gravitational-wave detector network will likely provide us with various gravitational-wave observations of binary neutron star systems. For an accurate interpretation of these detections, we need reliable gravitational-wave models. To test and to point out how existing models could be improved, we perform a set of high-resolution numerical-relativity simulations for four different physical setups with mass ratios $q$ = $1.25$, $1.50$, $1.75$, $2.00$, and total gravitational mass $M = 2.7M_\odot$ . Each configuration is simulated with five different resolutions to allow a proper error assessment. Overall, we find approximately 2nd order converging results for the dominant $(2,2)$, but also subdominant $(2,1)$, $(3,3)$, $(4,4)$ modes, while, generally, the convergence order reduces slightly for an increasing mass ratio. Our simulations allow us to validate waveform models, where we find generally good agreement between state-of-the-art models and our data, and to prove that scaling relations for higher modes currently employed for binary black hole waveform modeling also apply for the tidal contribution. Finally, we also test if the current NRTidal model to describe tidal effects is a valid description for high-mass ratio systems. We hope that our simulation results can be used to further improve and test waveform models in preparation for the next observing runs.