We dynamically self-assemble an active paramagnetic colloidal network that ballistically transports nonmagnetic fluorescent colloidal particles on top of the network. The transport mechanism is put into effect by a directed hydrodynamic flow, created by the rotation of individual colloids forming the network. The ballistic transport is confined to the network, and tracer beads in meshes show a diffusive instead of a ballistic transport. We develop a simple model to explain the transport.