If I search "general",
普通 and
一般 are at the top (#2 and #4, but
将軍 doesn't appear in the first page.
For comparison, they are the top 3 of Aedict.
Your #6 is
金, because the 10th definition or so is "golden general" (whatever that may or may not be).
So, yes, you have quite a conundrum, because common words have priority. But words whose definition matches better should also have priority, and here there are 2 aspects:
1-if the matching definition of one word is exactly the request, then it should trump the words which contain the request but diluted in a longer expression (if request="general" then
将軍 ("general") >
全スト ("general strike").
2- if the request is in the first or second definition of the word, then it should trump the words that have the request in the 6th, 8th or 10th definition
And by looking at the first page of results, I see
凱旋将軍. Well, this 3rd rule (that could be applied before?) would seem reasonable:
3- if 2 words match the request, but the first one is contained in the second one, the small one should always have priority on the compound.
And there's one (or two) more thing: I thought it could get better if I filter nouns only, but no,
将軍 is still out. And the "has sentences" doesn't work. Also, the filters take half of the space. I tapped a bit everywhere outside the filter zone before trying to tap the cog button again. Maybe if the cog button was colour-reversed (or another obvious colour change) when pressed down, it would be more intuitive.