A wellbore system for perforating a subterranean formation including a dissolvable perforating gun that may be wirelessly operated to fire at a predetermined wellbore location and thereafter fragmented and dissolved with wellbore fluids. The perforating gun may take the form of a strip gun with an elongated rod or other charge holder carrying a plurality of exposed perforating charges thereon. The exposed shaped charges may each be equipped with an individual charge cover or filler material disposed over a liner that forms a jet when the shaped charge is detonated. A wiper to facilitate pumping the perforating gun through the wellbore and may include an initiator for detecting a signal or condition indicative of the perforating gun having reached a predetermined location to cause the perforating gun to fire.