I cannot find a DXF code to store a 64-bit integer in the Extended Data. Is there any?
No, there is no DXF code to indicate a 64-bit value in Extended Data (XData). It is by design, because earlier AutoCAD versions wouldn't be able to read such a DWG file.
One workaround for this is to split your 64-bit value into two 32-bit values (high 32-bits and low 32-bits) and precede them with a code of your choosing to indicate to your application that they should be combined to 64-bit values.
Another workaround is using XRecords instead of XData, since there is support of kDxfInt64 in XRecords. When saving the XRecords back to 2007 and earlier formats, the 64-bit XRecord opcodes are converted into round-trip XData that is attached to the XRecord objects.