I presume the program will refer to Tablet XII of Gilgamesh, in which Enkidu visits the underworld and returns to the living world. This Babylonian tablet, which translates an earlier Akkadian poem is seen by most scholars as an appendix added to the original epic at a later date, since it varies enormously from the rest of the poem. For starters, Enkidu had been killed off back in Tablet VII, so having him alive again is a good indication that this was originally a separate poem.
At any rate, if a catabasis, or a descent to the underworld, is all it takes to be a "zombie," then Orpheus, Heracles, Theseus, and Odysseus must all be zombies, too. Needless to say, these Antique figures do not meet the modern definition of a reanimated, mindless corpse--a definition which descends, incidentally, not from the Classical catabasis but instead from the same source as the modern vampire, from the folkloric revenant or wraith, a corpse that rises from the grave to feed on the living.