Quartus 13.0sp1 supports compiling code for and programming the EPL7128SLC84-15 (I know because I have devices and do this). A USB Blaster JTAG programmer can program the devices, assuming you can get the requisite .pof file.
However that version of Quartus cannot read a device and save the programmed contents as a .pof. It can only program a device and then verify the programming. I believe you have to go back to MaxPlus 9.0 or so to get a version of the tools that can read a device contents.
In any event if the security bit is set in the device programming you will not be able to read the contents no matter what. Only erase and reprogram.
From your description it appears you are a customer of this design, and not the original developer who might have the .pof file. Which means you are likely SOL.