We study the dynamics of the 1D Hadamard quantum walk featuring generalized exponential correlated phase disorder. We report the existence of distinct dynamical regimes and discuss the prospect of a judicious tuning of the strength of localization of the walker via the degree of correlation. In particular, we unveil that when the typical correlation length is smaller than the chain size, the maximum spreading of the quantum wavepacket is achieved when the underlying disorder displays Gaussian correlations. Our work provides a framework for investigating the weakening of Anderson localization due to correlated disorder and may also find applications in the context of quantum information processing.