You say its a Brno VZ. 24? well that is where it was made, Brno, Czech. The E4 following the serial was 1937 according to my list but that is just one example. Another 4 digit number E4 is marked as 1935 but I think that is oddly out of order, but possible. 363 E4 is 1937. The list shows 7449 D4 as 1937 along with a couple C4 and B4's. The 4 indicates the number of times they have been thru the alphabet since production started in 1924. The 4F & G4 and even some F4's were made in 1937 also. 37-38 the Czech were producing more rifles then ever due to the situation with Germany. They never went above 4 digit serial numbers, exclusive of the pre-fix and suffix. So that is about 10,000 per letter. altho it is slightly less then our 26 letters.
Above the serial number there should be a small stamp E (lion symbol) 2 numbers. Those 2 numbers are the date rifle was inspected & excepted into the military. I will add your rifle to my data base with out any thing that would ID you, with your permission. Would like to know what is on receiver top and side rail to complete data.
Any other questions you may, have feel free to ask.
You can never go home again.