It depends on the context. If you are running a race, you could say: 'we must run/go from here' to indicate the start or beginning of the race. You could use the same expression to indicate the start of a journey, e.g. 'If we want to get there on time, we must go from here.' In this case, you would never use the word 'run', unless you were talking about a race of some kind. If you were advising someone to leave a place, you could say 'go from here'. A native speaker would be more likely to say 'get out of here', not 'go out of here', but it is not wrong to say 'go out of here'. Giving someone an instruction like 'run out of here' indicates urgency and the speaker wishes to convey that there is some kind of danger and that the person needs to get out of there fast.
So it all depends on context. If you would like to supply the context, I could give you a more specific answer.