Rubuta ci gaba don wannan sakin layi - Shekaru huɗu bayan haka, Heinz ya cancanci shiga tawagar Luxembourg ta biyu, a matsayin mai shekaru 23, a Wasannin Olympics na bazara na 2004 a Athens. Ta sami daidaitattun shigarwar B na 26.41 (50 m freestyle) da 57.14 (100 m freestyle) daga Taron Turai na Long Course a Luxembourg. A cikin mita 100 na 'yanci, Heinz ya fitar da Ágnes Mutina na Hungary don ɗaukar matsayi na biyar a zagaye na uku da talatin da shida a cikin duka ta 0.70 na biyu, tare da lokacin 57.40. A tseren mita 50 na 'yanci
, Heinz ya taɓa Ragnheiður Ragnarsdóttir na Iceland zuwa nasara ta biyar ta hanyar kashi ɗaya cikin ɗari (0.01), ya karya rikodin Luxembourg na 26.35 seconds. Nasarar da ta yi ba ta isa ba ta isa ta sanya ta ta shiga wasan kusa da na karshe, kamar yadda Heinz ya sanya na talatin daga cikin 'yan wasan 75 a cikin wasannin da suka gabata.