We fabricated microchip-sized Hydrogen (H) gas sensor based on a thin film of Iron-Palladium (FePd) alloy and investigated its ferromagnetic resonance (FMR) response in ambient and H gas environments and at atmospheric pressure. The fabricated sensing FePd alloy layers were 30 nm thick and their composition was 52% Fe and 48% Pd. Broadband stripline FMR spectroscopy was used to study the magnetization dynamics as a function of the stripline width. A comparative study was conducted between the FMR response of the continuous film and the film of finite width. Our results suggest that a significant increase in the FMR response was recorded for the narrower width stripline (50μm) samples compared with the FMR response of continuous film samples. In addition, we observed that sample annealing in nitrogen environment enhanced the FMR response by a factor of two. Furthermore, a very strong FMR signal of 80 μV in amplitude was recorded for nitrogen-annealed samples which, according to our best knowledge, is the highest amplitude of the FMR response ever recorded for FePd films at reasonable microwave powers (10dBm). Such a significant enhancement in the FMR response is believed to be a step forward towards commercial availability of a magnetic H gas sensor.