I don't think there are any quests doable at 37 - presumably with a group? - that will get you better than you can buy relatively cheaply.
A friend of mine, a warrior in much the same position, made enough grouping before LDoN to buy a couple of decentish weapons for around 500pp each.
With LDoN yielding maybe 50-100pp you could afford that kind of outlay. If you really had to you could probably solo spiderlings and make plenty from selling the silk in the bazaar. My 16 Paladin has just collected 100 Spider Silks which will fetch 500-100pp. I'm sure you could too.
If you are looking at things like a Copper Hamster of Striking - which is the current fashion in Warrior weapons - then it costs much, much more. But then you cannot quest anything remotely that good at 47 let alone 37.
You need fast weapons to hold aggro in the 30's and 40's. Just look at what you can afford in the bazaar. Prices vary from server to server but I am having trouble selling a Razor Edged Shgan'Tok (12/20) for 500pp atm. And don't forget the Weighty Polearm for 2HS. On most servers they are around 50-100pp.
If you are determined to quest because of the "achievement" factor then be prepared to get a weapon that is considerably below what you can buy.
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Wherever I go - there I am.