The mechanisms of infant development are far from understood. Learning about one's own body is likely a foundation for subsequent development. Here we look specifically at the problem of how spontaneous touches to the body in early infancy may give rise to first body models and bootstrap further development such as reaching competence. Unlike visually elicited reaching, reaching to own body requires connections of the tactile and motor space only, bypassing vision. Still, the problems of high dimensionality and redundancy of the motor system persist. In this work, we present an embodied computational model on a simulated humanoid robot with artificial sensitive skin on large areas of its body. The robot should autonomously develop the capacity to reach for every tactile sensor on its body. To do this efficiently, we employ the computational framework of intrinsic motivations and variants of goal babbling, as opposed to motor babbling, that prove to make the exploration process faster and alleviate the ill-posedness of learning inverse kinematics. Based on our results, we discuss the next steps in relation to infant studies: what information will be necessary to further ground this computational model in behavioral data.