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Neoclassical (NC) transport calculations are necessary for the complete simulation cycle of the behavior of plasmas inside both tokamaks and stellarators, which are more complex to be performed on the latest. In addition, due to the fact that the NC transport is mainly determined by the magnetic properties of the device (mathematically designed by the number of Fourier harmonics needed to describe the confining magnetic field), its study is mandatory to ensure the efficiency of a certain coil configuration before it is implemented in a fusion reactor. Thus, improvements to the already constructed devices and certain design decisions for the new ones, such as W7-X, NCSX, or QPS, have been made based on the estimations of the NC transport, among other criteria. In this sense, a compromise between the number of modes and polynomials to describe the distribution function and the required computing time to obtain reliable estimates is a must. This paper presents the porting process to the Grid and the computational optimization of the Drift Kinetic Equation Solver code, devoted to obtain the monoenergetic diffusion coefficients of the NC transport as well as the first coupled prototype for estimating the transport coefficients with such a new code release. The advantage of this code over the Monte Carlo applications already in production on the Grid is that it allows the estimation of all the transport coefficients, not only the diagonal ones. The tests and results obtained have been applied to the TJ-II Flexible Heliac, a stellarator in operation at National Fusion Laboratory (Spain), by using the EELA-2 Project infrastructure.