Distillation is an energy-intensive process, and it is vital that strategies are developed to improve these processes' sustainability. Synthesis of heat-integrated distillation sequences (HIDiS) plays a vital role in such a task. By identifying and integrating heat sources and sinks within distillation sequences, these configurations enable effective heat recovery and utilization, leading to reduced energy consumption and environmental impacts. The present work presents a new superstructure-based model with a Pinch-based operator for implicit heat integration (i.e., prediction of heat integration costs) and a stochastic solution approach for developing efficient HIDiS. Explicit heat integration (definition of heat exchanger matches) is then performed in the second part of the method. Two examples in the literature were used to validate the method. In both cases, the strategy presented was able to attain solutions with better total annual costs than those from the literature (15.8 and 11.5% lower). Solutions found with the present approach presented a greater degree of heat integration than those from the literature: more heat recovery units are present with considerably greater total heat duty (about twice greater in example 1, for instance).