This paper presents the aerodynamic shape optimization of the MEXICO wind turbine (WT) blade, targeting the maximization of the axial moment and, hence, of the produced power. The optimization is conducted using the OpenFOAM-based continuous adjoint solver named adjointOptimisationF oam, developed and made publicly available by the group of authors. This implements and solves the adjoint to the Navier-Stokes system of equations, coupled with the differentiation of the Spalart-Allmaras turbulence model. Herein, this was extended to include the adjoint to the flow equations which are solved for the absolute velocity in the relative reference frame. Challenges in the convergence of the adjoint equations, mostly attributed to flow unsteadiness causing marginal convergence of the steady flow solver, are treated by additionally implementing the Recursive Projection Method (RPM). Assessment of the adjoint sensitivities with finite differences in a similar 2D case is also included. Then, the flow solution for the MEXICO WT case is compared with the outcome of another CFD solvers and experimental data, prior to the application of the expanded optimization software to maximize the axial moment of the WT. The blade and the displacement of the surrounding grid nodes are parameterized using a volumetric B-Splines morphing box. The optimization designed a blade bended in the axial direction axial moment, having a higher by 10.8%.