Using a combination of muon-spin relaxation (mu SR), inelastic neutron scattering (INS), and nuclear magnetic resonance (NMR), we investigated the novel iron-based superconductor with a triclinic crystal structure (CaFe1-xPtxAs)(10)Pt3As8 (T-c = 13 K), containing platinum-arsenide intermediary layers. The temperature dependence of the superfluid density obtained from the mu SR relaxation-rate measurements indicates the presence of two superconducting gaps, Delta(1) >> Delta(2). According to our INS measurements, commensurate spin fluctuations are centered at the (pi, 0) wave vector, like in most other iron arsenides. Their intensity remains unchanged across T-c, indicating the absence of a spin resonance typical for many Fe-based superconductors. Instead, we observed a peak in the spin-excitation spectrum around (h) over bar omega(0) = 7 meV at the same wave vector, which persists above T-c and is characterized by the ratio (h) over bar omega(0)/k(B)T(c) approximate to 6.2, which is significantly higher than typical values for the magnetic resonant modes in iron pnictides (similar to 4.3). The temperature dependence of magnetic intensity at 7 meV revealed an anomaly around T* = 45 K related to the disappearance of this new mode. A suppression of the spin-lattice relaxation rate, 1/T1T, observed by NMR immediately below T* without any notable subsequent anomaly at T-c, indicates that T* could mark the onset of a pseudogap in (CaFe1-xPtxAs)(10)Pt3As8, which is likely associated with the emergence of preformed Cooper pairs.