034 is not a country code. Numbers inside a country start like this: Kanchanaburi/Nakhon Pathom/Samut Sakhon/Samut Songkhram (Thailand), Kragujevac (Serbia), Burgdorf/Langnau i.E. (Switzerland), Abadia dos Dourados - MG (Brazil) and others. The first digit 0 is the trunk prefix for domestic calls and is dropped from abroad.
If a number starts with +, the first 1–3 digits are the country code. If it starts with 0 (8 in Russia and Kazakhstan), it is a domestic number: an area or operator code follows, and from abroad the 0 or 8 is replaced with + and the country code. The same digits can mean different places, so where the call came from matters.