Instantaneous or statistical channel state information (CSI) is needed for most detection schemes developed for molecular communication (MC) systems. Since the MC channel changes over time, e.g., due to variations in the velocity of flow, the temperature, or the distance between transmitter and receiver, CSI acquisition has to be conducted repeatedly to keep track of CSI variations. Frequent CSI acquisition may entail a large overhead whereas infrequent CSI acquisition may result in a low CSI estimation accuracy. To overcome these challenges, we design codes which enable maximum likelihood sequence detection at the receiver without instantaneous or statistical CSI. In particular, assuming concentration shift keying modulation, we show that a class of codes, referred to as strongly constant-weight (SCW) codes, enables optimal CSI-free sequence detection at the expense of a decrease in data rate. For the proposed SCW codes, we analyze the code rate, the error rate, and the average number of released molecules. In addition, we study the properties of binary SCW codes and balanced SCW codes in further detail. Simulation results verify our analytical derivations and reveal that SCW codes with CSI-free detection outperform uncoded transmission with optimal coherent and non-coherent detection.