This work presents the application of the omni-aiNet algorithm - an immune-inspired algorithm originally developed to solve single and multiobjective optimization problems - to the construction of phylogenetic trees. The main goal of this work is to automatically evolve a population of phylogenetic unrooted trees, possibly with distinct topologies, by minimizing at the same time the minimal evolution and the mean-squared error criteria. The obtained set of phylogenetic trees contains non-dominated individuals that form the Pareto front and that represent the trade-off of the two conflicting objectives. The proposal of multiple non-dominated solutions in a single run gives to the user the possibility of having distinct explanations for the difference observed in the terminal nodes of the tree, and also indicates the restrictive feedback provided by the individual application of well-known algorithms for phylogenetic reconstruction that takes into account both optimization criteria, like Neighbor Joining.