Methods for generative design of robot physical configurations can automatically find optimal and innovative solutions for challenging tasks in complex environments. The vast search-space includes the physical design-space and the controller parameter-space, making it a challenging problem in machine learning and optimisation in general. Evolutionary algorithms (EAs) have shown promising results in generating robot designs via gradient-free optimisation. Morpho-evolution with learning (MEL) uses EAs to concurrently generate robot designs and learn the optimal parameters of the controllers. Two main issues prevent MEL from scaling to higher complexity tasks: computational cost and premature convergence to sub-optimal designs. To address these issues, we propose combining morpho-evolution with intrinsic motivations. Intrinsically motivated behaviour arises from embodiment and simple learning rules without external guidance. We use a homeokinetic controller that generates exploratory behaviour in a few seconds with reduced knowledge of the robot's design. Homeokinesis replaces costly learning phases, reducing computational time and favouring diversity, preventing premature convergence. We compare our approach with current MEL methods in several downstream tasks. The generated designs score higher in all the tasks, are more diverse, and are quickly generated compared to morpho-evolution with static parameters.