Using TWKHH on your shipping documents
Carriers print the port of loading and port of discharge on bookings and bills of lading as UN/LOCODEs, so TWKHH is what you will normally see against Kaohsiung on carrier paperwork and in schedule and tracking feeds. The first two characters, TW, are the ISO 3166-1 country code for Taiwan (Province of China); the remaining three identify the place within it.
A UN/LOCODE names a place, not a berth. Where a port city runs several container terminals, UNECE often assigns the terminals their own codes alongside the city code — which is why a booking can legitimately show a code you did not expect. Take the code from the carrier booking rather than picking the one that reads most like the port name.
Schedule D codes are a US-only system, so Kaohsiung does not have one. If Kaohsiung is your origin, the Schedule D code that matters is the one for your US port of entry — every US port page in this tool shows it where CBP publishes it.
Kaohsiung carries the airport classifier in UN/LOCODE, but the code list does not supply an IATA code for it. We do not infer one: the last three characters of a UN/LOCODE often match the IATA code but are not required to, and a wrong code on an air waybill is expensive. Take the IATA code from your airline or forwarder.