If you already have the PLC connected to LAN, you can connect the HMI to the same LAN, if it's not already done.
Anyway I hope you mean the factory intranet and not internet, as it's not wise to open up machines for access from internet...
If you insist doing it by the PLC you will get only the alarm, warning and information messages... nothing about what the machine is doing, or what the operator might be doing.
If your machine has a Krones LDS (Line Diagnostis System) you could get some basic information, lige state, and program etc. but it will be a long road to combine this into a monitoring system that will be useful (in my opinion).
But lets go a bit deeper

From the little part of the DB you provided it looks like the DB63 is structured using an UDT
The BYTE "index" contains the alarm index (the message number I believe)
The Bit 0 "is_active" is 1 if the alarm is active
The Bit 1 "is_gone" is 1 if the alarm has been active but still not reset
Alarm number 2001.6311 I would read as area 2001 (usually also a reference in the hardware drawing) the 6311 is the message number (the number you should be able to find in the Zenon Language txt-file).
Your machine is not too old, so the structure is unfortunately not as simple as I first believed... the entire list consists of data from several DB's
To find each individual alarm/warning/message reference, you should search the Step7 program for all locations of the following blocks:
FC115, FC116, FC117, FC118 and FC119 as they generate the output to the Zenon.
Scearch for the DB63.DBX91.0 and you should be able to find where it triggers one of the above mentioned FC's and you should be able to figure out the rest

The mentioned FC blocks are for different level of details:
FC115 Simple message without extra information
FC116 Simple message
FC117 Message with 3 additional data
FC118 Message with extra variables
FC119 Message with 5 additional data
Note the block numbers could be different in your machine (I have only mixer and CIP that new).
As you probably know by now, this is a lot of work! so I would suggest to explore the option mentioned first, and connect to the Zenon HMI via VNC
The HMI is probably a PC with Windows7 Embedded and Zenon RT, 2 LAN connections... one could easily be used for your intranet (if it's not already connected). Using a VNC client, the HMI IP address, probably port 5900 or 5901 and the password, you should soon be able to sit in your comfortable quiet office with popcorn and a cool Coke, watching the machine filling bottles/cans in the noisy production area

Good luck
