I just want to make sure I understand your question. You are outputting current from the PCI-6704 which is connected to your DUT. When the DUT changes such that it looks like an open circuit to the PCI-6704 you see spikes on the current output lines of the PCI-6704. Correct?
If so, what current are you outputting from the PCI-6704? What is the level of the spikes compared to the level of the current? What is the duration of the current spike? What is the frequency of the spikes? How are you cabling the PCI-6704 to your DUT?