You may access the underlying QuadDec_Count8 and generate interrupts. But I am afraid you will just get some numbers in a row.
I wonder why you want to "store" quadrature decoder values. Usually this data is used in real time for motion control. But if you need to store it, how long do you need to store it -- a few seconds? You could read the data from DMA to an array for processing. If you need to store it for a long time or transfer to an external device, you could use a serial interface UART, SPI, I2C to transfer to an SD card or whatever.