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The correct quantification of the dose released in charged particle therapy treatments requires the knowledge of the double differential fragmentation cross section of particles composing both the beam and the target. The FragmentatiOn Of Target (FOOT) experiment aims at measuring these cross sections for ions of interest for charged particle therapy applications. This article describes the performance of the time-of-flight (TOF)-wall detector of the experiment. The detector is composed of two layers of 44 cm $\times 2$ cm $\times 3$ mm plastic scintillator bars (20 for each layer), arranged orthogonally and read-out by silicon photomultipliers. The detector is designed to identify the charge of fragments ranging from protons to oxygen ions, with a maximum energy of 700 MeV/u, by measuring the energy released in the scintillators and the TOF with respect to a start counter. In this study, the detector was scanned with carbon ions of energy between 115 and 400 MeV/u and with a 60-MeV proton beam. The measurements show an energy resolution ($\sigma _{E}/\mu _{E}$) between 6% and 4% and a contribution of the detector to the TOF system time resolution between 25 and 20 ps (standard deviation) for carbon ions and between 100 and 80 ps for protons. [ABSTRACT FROM AUTHOR]