The totally asymmetric simple exclusion process (TASEP), which describes the stochastic dynamics of interacting particles on a lattice, has been actively studied over the past several decades and applied to model important biological transport processes. Here we present a software package, called EGGTART (Extensive GUI gives TASEP-realization in real time), which quantifies and visualizes the dynamics associated with a generalized version of the TASEP with an extended particle size and heterogeneous jump rates. This computational tool is based on analytic formulas obtained from deriving and solving the hydrodynamic limit of the process. It allows an immediate quantification of the particle density, flux, and phase diagram, as a function of a few key parameters associated with the system, which would be difficult to achieve via conventional stochastic simulations. Our software should therefore be of interest to biophysicists studying general transport processes, and can in particular be used in the context of gene expression to model and quantify mRNA translation of different coding sequences.