A good safety culture comes from one that is perceived to be just. How to get that just culture and maintain it is enough work for a PhD thesis, which also indicates how many people know what an effective just culture is.
But it's safe to say that you have to have everyone on board singing from the same song sheet. That's the management, the pilot's union (representing the workforce) and the safety system, assuming if it's separate from the management of the company - which it needs to be if it's going to be effective. You need a clearly defined process which is adhered to if there is an event to investigate. And the safety reporting system needs to be open, transparent and free from disciplinary action, unless there is a wilful disregard for the rules - the response to which will be defined by the process I have just mentioned. There is plenty of information in aviation which has had a lot of success in this field. Please feel free to PM me if you want to discuss further.
But take this on baord. It can take years to build a just culture and only one day to destroy it if you handle an incident incorrectly. You have to get this right and be seen to get it right.