Modular robots have captured the interest of the robotics community over the past several years. In particular, many modular robotic systems are reconfigurable, robust against faults, and low-cost due to mass production of a small number of different homogeneous modules. Faults in these systems are normally tolerated through redundancy or corrected by discarding damaged modules, which reduces the operational capabilities of the robot. To overcome these difficulties, we previously developed and discussed the general design constraints of a heterogeneous modular robotic system (Hex-DMR II) capable of autonomous team repair and diagnosis. In this paper, we discuss the design of each module, in detail, and present a new, novel elevator module. Then, we introduce a forestlike structure that enumerates every non-isomorphic, functional agent configuration of our system. Finally, we present a case study contrasting the kinematics and power consumption of two particular configurations during a mapping task.