This paper presents a grammatical evolution (GE)-based methodology to automatically design third generation artificial neural networks (ANNs), also known as spiking neural networks (SNNs), for solving supervised classification problems. The proposal performs the SNN design by exploring the search space of three-layered feedforward topologies with configured synaptic connections (weights and delays) so that no explicit training is carried out. Besides, the designed SNNs have partial connections between input and hidden layers which may contribute to avoid redundancies and reduce the dimensionality of input feature vectors. The proposal was tested on several well-known benchmark datasets from the UCI repository and statistically compared against a similar design methodology for second generation ANNs and an adapted version of that methodology for SNNs; also, the results of the two methodologies and the proposed one were improved by changing the fitness function in the design process. The proposed methodology shows competitive and consistent results, and the statistical tests support the conclusion that the designs produced by the proposal perform better than those produced by other methodologies.