Unicode characters from charcode in javascript for charcodes > 0xFFFF

I need to get a string / char from a unicode charcode and finally put it into a DOM TextNode to add into an HTML page using client side JavaScript.

Currently, I am doing:

String.fromCharCode(parseInt(charcode, 16));

where charcode is a hex string containing the charcode, e.g. "1D400". The unicode character which should be returned is