Thanks to ground-based infrared and submillimeter observations the study of the dusty torus of nearby active galactic nuclei has greatly advanced in the last years. With the aim of further investigating the nuclear mid-infrared emission of the archetypal Seyfert 2 galaxy NGC 1068, here we present a fitting to the N- and Q-band Michelle/Gemini spectra. We initially test several available spectral energy distribution (SED) libraries, including smooth, clumpy and two-phase torus models, and a clumpy disk+wind model. We find that the spectra of NGC 1068 cannot be reproduced with any of these models. Although, the smooth torus models describe the spectra of NGC 1068 if we allow variation of some model parameters among the two spectral bands. Motivated by this result, we produced new SEDs using the radiative transfer code SKIRT. We use two concentric tori that allow us to test a more complex geometry. We test different values for the inner and outer radii, half-opening angle, radial, and polar exponent of the power-law density profile, opacity, and viewing angle. Furthermore, we also test the dust grains' size and different optical and calorimetric properties of silicate grains. The best-fitting model consists of two concentric components with outer radii of 1.8 and 28 pc, respectively. We find that the size and the optical and calorimetric properties of graphite and silicate grains in the dust structure are key to reproducing the spectra of NGC 1068. A maximum grain size of 1 μm leads to a significant improvement in the fit. We conclude that the dust in NGC 1068 reaches different scales, where the highest contribution to the mid-infrared is given by a central and compact component. A less dense and extended component is present, which can be either part of the same torus (conforming a flared disk) or can represent the emission of a polar dust component, as already suggested from interferometric observations.