A recently developed beam telescope, consisting of four Micromegas detectors with standard copper anodes of 360 strips and an active area of $9\,\mathrm{cm}\times10\,\mathrm{cm}$, has been tested in 160\,GeV pion and 140\,GeV muon beams at the SPS at CERN. The 1500 anode-channels of 250 $\mu$m strip pitch are read out using a Gassiplex-frontend based electronics, originally developed for the HADES RICH detector, that has been adapted to the negative Micromegas signals. The telescope was operated stably over several weeks with an efficiency close to 100\%. Collecting around 20 million pion and muon tracks, two different Ar:CO$_2$ gas mixtures, 93:7 and 85:15, have been tested at 1016\,mbar. The dependence of the single detector spatial resolution on a variety of parameters has been investigated. For both gas mixtures a best value of 35\,$\mu$m is reached by maximizing the number of electrons entering the amplification region. The resolution depends only weakly on the gas-gain. The combination of four detectors allows thus for a track accuracy of 20\,$\mu$m. The discharge rate in the pion beam with a flux-density of 4 kHz/cm$^2$ was around $10^{-5}$ per pion and thus negligible, the discharge rate was even smaller for muons. The development of a $48\,\mathrm{cm}\times50\,\mathrm{cm}$ Micromegas detector with floating strip technology for improved discharge behavior in densely-ionizing neutron and proton beams is ongoing.