The Fast Timing Micro-Pattern Gaseous Detector (FTM) has been recently introduced as a promising alternative for applications that require improved time resolution, such as high-luminosity accelerators and medical imaging. The FTM consists of a stack of several coupled gas layers alternating drift and multiplication stages. The time resolution is determined by the time of the fastest signal among all amplification stages, read out by external electrodes through capacitive couplings. In the present work, we use the Garfield++ simulation toolkit in order to investigate and optimize the FTM performances. Gain, timing, and efficiency of the FTM are studied as a function of different parameters, such as detector geometry, gas mixture, and applied electric fields. The simulations that are presented in this paper show that a time resolution as low as 160 ps can be reached with a 32-layers FTM.