Eugeniu Cociuc moved to Pyunik from the Moldovan club Zimbru in 2022. In the 2021/22 season, Eugeniu became the winner of the Armenian championship with Pyunik. Cociuc won the first cup of his career in 2016, becoming the champion of Slovakia with Žilina. The Moldovan footballer played only in European clubs. Cociuc is a football player of the Moldova national team, from where he received his first invitation in 2015 and played 25 matches.