The 942-Memory Training Errors, with various codes (1501, 301C, 3016), have been encountered in several HP Z-series workstations - Z420, Z620 and (my own) Z820, since the introduction of Intel's family of microprocessors early in 2012.
This type of error is usually accompanied by a large number of repeated WHEA (Windows Hardware Errors) Warning Events in Windows 7 Event Viewer:
Event ID 47 - Memory, Corrected Machine Check and Event ID 20 - Microsoft-Windows-Kernel-WHEA/Errors.
I recommend that you verify it in the Event Viewer in your Z620 after booting Windows 7.
No 'Memory Diagnostics' could find the error; but it kept appearing at every booting.
There are two 'workarounds' that I tried:
1. Similar to recommendation in HP Customer Advisory: URL:
http://h20564.www2.hpe.com/hpsc/doc/public/display?docId=emr_na-c03282091 :
In the BIOS Setup (F10) of the Z620 Workstation, in 'OS Power Management', change 'Idle Power Savings' from 'Extended' to 'Normal', and see that 'S5 Maximum Power Savings' is set to 'Disabled'; by this I managed to reduce the rate of WHEA warnings in Windows 7 Event Viewer from thousands per second down to a few dozen.
Yet, this workaround alone still did not prevent the '942 - Memory Training Error' on every booting of my HP Z820.
2. Having moved the suspected Memory DIMM among slots and seeing that the location of the 942 error followed the location of the DIMM, I informed HP Support and their technician verified my findings and replaced the faulty Memory DIMM with a new one. (I have purchased extended warranty for my Z820).
A similar chain of events occurred in my Z820 workstation several times between 2013 and 2016,
and I expect to encouner it again during the prospected life of the workstation.
As your Z620 is now out of warranty, you will probably have to experiment with various types of replacement Memory DIMMs before the '942 - Memory Training Error' goes away for a few months or more.