Contact detection, which is the process of detecting if two particles are in contact, is a step that takes a significant part of the simulations such as Molecular Dynamics (MD) or Discrete Element Method (DEM). The Linked Cells algorithm is a popular method for contact detection, but it becomes inefficient when dealing with simulations containing particles of varying sizes. In this paper, we present the shared-memory parallelization and implementation of the Hierarchical Grid algorithm for contact detection in the AutoPas library, enabling efficient contact detection for simulations with diverse particle sizes. We describe two strategies for parallelizing the Hierarchical Grid algorithm: one using OpenMP tasks and other using simple OpenMP parallel for work sharing. Additionally, we integrate dynamic cutoffs that are based on Lennard-Jones particles sigma values into md-flexible, a Molecular Dynamics simulation program that uses AutoPas. Our results demonstrate that the Hierarchical Grid implementation outperforms existing Linked Cells implementation on simulations with high density of small particles. However, we observe that the parallel scaling of our implementation is suboptimal on high thread counts.