The proton charge radius can be determined by measuring the slope of the electric form-factor $G_E$ at small four-momentum transfer squared $Q^2$. Numerous elastic-scattering and laser-spectroscopy measurements of the proton radius have been performed with contradicting results, often referred to as the proton-radius puzzle. We propose to measure the proton charge radius in high-energy elastic muon-proton scattering at the M2 beam line of CERN's Super Proton Synchrotron (SPS) in 2022. A high-precision measurement at low $Q^2$, performed with a high-pressure hydrogen-filled time-projection chamber (TPC), can contribute to the resolution of the puzzle, especially due to the different systematic effects of this approach compared to those of electron-proton scattering. In 2018, we performed a test measurement with silicon tracking detectors up- and downstream of a prototype TPC to study the feasibility of the measurement concept. We present initial results of the on-going analysis of the test data and discuss ideas for a possible experiment at CERN in 2022.