  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 proceeding the
minimization of the total energy, this way introducing the corresponding energy
lower-bound, such a construction being only possible due to a differential
constraint including 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. In the sequel, in order to solve these
equations, we choose the dielectric function explicitly, also calculating the
corresponding self-interacting potential. We impose appropriate boundary
conditions supporting nontopological solitons, from which we verify that the
energy of final structures is proportional to the magnetic flux they engender,
both quantities being not quantized, as expected. We depict the new numerical
solutions, whilst commenting on the main properties they present.
