Z38.0 requires a 5th digit required and you are likely to get claims rejected or denied for billing without the 5th digit. There only 2 codes in this range:
Z38.00-Single liveborn infant, delivered vaginally.
Z38.01-Single liveborn infant, delivered by cesarean.
Per Encoder Pro: Range "Z38": These codes are used as the principal diagnosis on all newborn birth records and only for that first birth encounter. The codes in this category capture whether the newborn was a single birth or part of a multiple birth, whether the delivery was vaginal or cesarean, and whether or not the newborn was born inside or outside of the hospital.
I think it is correct to use the Z38.00 & Z38.01 codes based on this information rather than Z76.2 or Z00.1.