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Check here manual(Converting Databases to 64-bit Oracle Database Software).
You will need to install the 64-bit 220.127.116.11 software on the new server (pay heed to the pre-reqs), then apply the same patches to 18.104.22.168 that you applied on the old server, then follow the process in the link posted above.
Oracle Database (RDBMS) on Unix AIX,HP-UX,Linux,Mac OS X,Solaris,Tru64 Unix Operating Systems Installation and Configuration Requirements Quick Reference (8.0.5 to 11.2) [ID 169706.1]
How to Convert a 32-bit Database to 64-bit Database on Linux? [ID 341880.1]