  We study the most general Two Higgs Doublet Model with $SU(2)$ gauge fields
on the lattice. The phase space is probed through the computation of
gauge-invariant global observables serving as proxies for order parameters. In
each phase, the spectrum of the theory is analysed for different combinations
of bare couplings and different symmetry breaking patterns. The scale setting
and determination of the running gauge coupling are performed through the
Wilson flow computation of the action density.
