We consider nontopological first-order solitons arising from a gauged CP(2) model in the presence of the Maxwell term multiplied by a nontrivial dielectric function. We implement the corresponding first-order scenario by minimizing the total energy, thus introducing the corresponding energy lower bound; such a construction is only possible due to a differential constraint that includes the dielectric function itself and the self-interacting potential defining the model. We saturate the aforementioned bound by focusing our attention on those solutions fulfilling a particular set of two coupled first-order differential equations. Next, in order to solve these equations, we choose the dielectric function explicitly, and also calculate the corresponding self-interacting potential. We impose appropriate boundary conditions that support nontopological solitons, from which we verify that the energy of final structures is proportional to the magnetic flux they engender: both quantities are not quantized, as expected. We depict the new numerical solutions, while commenting on the main properties they present.