We present a new multi-fluid, grid-based magnetohydrodynamics (MHD) code PIERNIK, which is based on the Relaxing Total Variation Diminishing (RTVD) scheme (Jin & Xin 1995). The original scheme (see Trac & Pen 2003 and Pen et al.  2003) has been extended by an addition of dynamically independent, but interacting fluids: dust and a diffusive cosmic ray (CR) gas, described within the fluid approximation, with an option to add other fluids in an easy way. The code has been equipped with shearing-box boundary conditions, a selfgravity module, an Ohmic resistivity module, as well as other facilities which are useful in astrophysical fluid-dynamical simulations. The code is parallelized by means of an MPI library. In this paper we introduce a multifluid extension of the RTVD scheme and present a test case of dust migration in a two-fluid disk composed of gas and dust. We demonstrate that due to the difference in azimuthal velocities of gas and dust and the drag force acting on both components, dust drifts towards maxima of the gas pressure distribution.