ENC28J60 does not embed the TCP/IP stack. It only has ethernet PHY and MAC included.
So, even for the most simple (UDP) you'll need need to write / use the basic services of a TCP/IP stack :
IP protocole, UDP protocole, ARP protocole...etc...
If you want to do it by yourself, expect to spend some months.
The other alternative is to use TCP/IP lite from MCC on one of the supported MCUs (PIC16 / PIC).
This document explains very how much flash and RAM you'll need depending on which protocole your want to use :http://ww1.microchip.com/downloads/en/DeviceDoc/release_notes_TCPIPLite_library_v2_2_11.pdf
If you want to use PIC18F27K42, it will definitely work
because it has large RAM / large FLASH
For simple stack I suggest : ARP, DHCP, IP, UDP (first in the table of the document)