  We present a new two-dimensional numerical code called Nada designed to solve
the full Einstein equations coupled to the general relativistic hydrodynamics
equations. The code is mainly intended for studies of self-gravitating
accretion disks (or tori) around black holes, although it is also suitable for
regular spacetimes. Concerning technical aspects the Einstein equations are
formulated and solved in the code using a formulation of the standard 3+1 (ADM)
system, the so-called BSSN approach. A key feature of the code is that
derivative terms in the spacetime evolution equations are computed using a
fourth-order centered finite difference approximation in conjunction with the
Cartoon method to impose the axisymmetry condition under Cartesian coordinates
(the choice in Nada), and the puncture/moving puncture approach to carry out
black hole evolutions. Correspondingly, the general relativistic hydrodynamics
equations are written in flux-conservative form and solved with
high-resolution, shock-capturing schemes. We perform and discuss a number of
tests to assess the accuracy and expected convergence of the code, namely
(single) black hole evolutions, shock tubes, and evolutions of both spherical
and rotating relativistic stars in equilibrium, the gravitational collapse of a
spherical relativistic star leading to the formation of a black hole. In
addition, paving the way for specific applications of the code, we also present
results from fully general relativistic numerical simulations of a system
formed by a black hole surrounded by a self-gravitating torus in equilibrium.
