We present the C++ library ggxy, which can be used for the fast and flexible calculation of partonic and hadronic cross sections to gluon-initiated top-mediated processes such as $gg\to HH$, as well as the newly derived processes $gg\to ZH$ and $gg\to ZZ$, at NLO QCD including full top-quark mass dependence. The two-loop virtual amplitudes are implemented using analytical approximations in different kinematic regions, while all other parts of the calculation are exact. This implementation allows to freely modify all input parameters, such as the top-quark mass and its renormalization scheme and the masses of the external $Z$/Higgs bosons. In addition, ggxy has been interfaced to Powheg, which allows the matching to parton showers.