  In light of the ongoing effort on reducing the theoretical uncertainties and
an upcoming experiment concerning muon magnetic moment, we perform a detailed
study of an 3-4-1 electroweak gauge extension of the standard model that
contains exotic charged leptons in its spectrum. We discuss flavor changing
neutral current, collider and electroweak bounds on the model and derive
$1\sigma$ limits using current and projected limits on the muon magnetic
moment. In summary, we exclude the masses of new gauge bosons that couple to
muons and heavy charged leptons up to $700$~GeV. Moreover, we find a projected
lower bound on the scale of symmetry breaking to be $2$~TeV.
