Massive gas injections are proposed as a means to mitigate the formation of a runaway current of relativistic electrons that may result from a disruption in tokamak plasmas. The effective use of this mitigation scheme demands a detailed understanding of the mechanisms of runaway current formation and dissipation. In this paper we present simulations of disruptions in the tokamak ASDEX Upgrade using kinetic modeling, and demonstrate that these models capture important aspects of the runaway current formation and dissipation. Measured values of electron temperature, plasma current, free electron density and amount of injected argon are used as input to the simulations and the resulting calculated current density is compared with the evolution of the measured total current. The onset of the current decay is accurately captured, as well as the current decay rate during and after the disruption. CODE hence shows a potential to be useful, in combintaion with other codes, for the modeling of disruptions in the presence of massive gases.