Javi -
did you try setting the Chip Status Control Register to (for example 0x21) and then ISO protocol register to (for example 0x02) and then sending the inventory command?
0x8F, 0x91, 0x3D, 0x00, 0x03, 0x26, 0x01, x00
then you will wait on EOTX IRQ, service that, clear the FIFO, with a dummy clk; then get EORX IRQ, service that, read the FIFO status register (value = n-1, so add 1 to the number), then read out FIFO for that number of bytes? (should be 10 there as response to ISO15693 inventory command is: 0x00 (no error response flags) + DSFID (default is 0x00) + UID (8 bytes, LSByte first)