Typical methods of quantum/reversible synthesis are based on using the binary character of quantum computing. However, multi-valued logic is a promising choice for future computer technologies, given a set of advantages when comparing to binary circuits. In this work, we have developed a genetic algorithm-based synthesis of ternary reversible circuits using Muthukrishnan-Stroud gates. The method for chromosomes coding that we present, as well as a judicious choice of algorithm parameters, allowed obtaining circuits for half-adder and full adder which are better than other published methods in terms of cost, delay times and amount of input ancillary bits. A structure of the circuits is analyzed in details, based on their decomposition.