Recently new message passing decoders for LDPC codes, called finite alphabet iterative decoders (FAIDs) were proposed. The messages belong to a finite alphabet and the update functions are simple boolean maps different from the functions used for the belied propagation (BP) decoder. The maps can be chosen using the knowledge of potential trapping sets such that the decoders surpass the BP decoder in the error floor. In this paper, we address the issue of selecting good FAIDs which perform well in the error floor for column weight three codes. We introduce the notion of noisy trapping set which is a generalization based on analyzing the local dynamic behaviour of a given FAID on a trapping set. Using this notion as the core, we provide an iterative greedy algorithm that outputs a set of candidate FAIDs containing potentially good decoders for any given code. To illustrate the appliance of the methodology on several codes, we show that the set of candidate FAIDs contains particularly good FAIDs for different codes with different rates and lengths.