A major hurdle in machine learning is scalability to massive datasets. Approaches to overcome this hurdle include compression of the data matrix and distributing the computations. \textit{Leverage score sampling} provides a compressed approximation of a data matrix using an importance weighted subset. \textit{Gradient coding} has been recently proposed in distributed optimization to compute the gradient using multiple unreliable worker nodes. By designing coding matrices, gradient coded computations can be made resilient to stragglers, which are nodes in a distributed network that degrade system performance. We present a novel \textit{weighted leverage score} approach, that achieves improved performance for distributed gradient coding by utilizing an importance sampling.