Hello Georg Taschl,
the record is in Latin. so you should add latin to the tags.
I would read "Maria, Laurentij Codgunes", but in genitive case.
Later as godparent: "Georgius Codgune"
So I would suggest Laurent(ius) Codgune as bride's father and "Georg(ius) Codgune" as godparent.
If I would have other sources with Laurent I would take Laurent, otherwise, I think I would take Laurentius.
But the family name is Codgune.