Heinz started his football career in his native Czech Republic, where he played for Lázně Bohdaneč and Sigma Olomouc before moving to Germany in 2000.
In international tournaments, he has been many times a winner, taking outright or shared first prize at Cerveny Kostelec 1959, Prague 1968, Madonna di Campiglio 1973, Amsterdam 1974, Vrnjacka Banja 1981, Trnava 1982, Borgarnes 1985, Gausdal 1987 (and twice in 1988), Badenweiler 1990, Munster 1992 and Lazne Bohdanec 1997.