We present an experimental study of the generation of strongly localized structures that propagate on the surface of a dissipative fluid. We excited a layer of fluid with a vertical periodic acceleration field, and a parametric instability occurs when a certain threshold value is achieved. This process is known as Faraday Instability and the temporal evolution of the system obeys a period-doubling route. For a highly dissipative fluid we observed two new interesting phenomena: the generation of high spatially localized structures which propagate on top of the stripes of stationary pattern, and a periodic window which occurs after the system reached spatiotemporal chaos.