First, what's a quadruple negative!?

Second...
Admittedly, English is a language where since primary school I have been thought that double negatives are a bad thing
Just prescriptively. It varies by dialect.. in Standard English they're "bad" (according to prescriptivists) or "ungrammatical" (according to descriptivists). Certainly they are ungrammatical for me, but I've been exposed to them in other (perhaps sometimes fictionalized) dialects. In Southern American English, they're pretty common. They might even appear emphatically or colloquially elsewhere in some idioms.
Hmm, now that you've peaked (is that the right word) my interest, why exactly are double negatives "bad" in English? And do double negatives only involve "not", or are there other constructs?
They're not bad. They're just nonstandard. So "y'all" and double negatives are the same kind of thing. Nonstandard, Southern American English (among other varieties) that are socially stigmatized.
They're also "illogical" because they're not found in Latin (although, wait, they are found throughout the Romance languages... I wonder....), and because they're "logically positive"--
-(-1)=1, so it's assumed they should not be used.
But getting to the point, "miss not" is far from a typical double negative in English. I didn't mean to suggest that. I meant quite literally that it seems to have two negatives being used where one would be sufficient, internal to the grammar.
A typical double negative is "not" plus a negative quantifier:
There isn't no one here.
I didn't buy no bread.
We don't do that never.
etc.
Typically, fictionally, they're portrayed with "ain't":
We ain't got no money!
etc.
Obviously that's a stereotype.
From the little I know about double negatives in English, I think they're found in various dialects (eg, in England) and not just in the Southern part of the US, but they are (for me) known popularly to be found there. It's one of the obvious and imitated characteristics.
Now, interestingly enough, what I believe is that these actually aren't double negatives, at least in some cases. What happens is that in some languages/dialects there's a distinction between the negative word "no" and the negative polarity item (NPI) "any", even though they have identical semantics.
So the word "no" is simply used more widely in languages/dialects that have "double negatives". It's actually the lack of a special NPI that causes this, not some misuse of "no".
peaked (is that the right word)
It's
piqued but it is the right word. (Actually,
as a native speaker, I just figured out that spelling a month or two ago-- I remember looking it up.) (Seems like a great one for a folk etymology, though-- "brought my interest to a peak". I think it comes from a French root meaning something about pinching/poking, like Spanish "picar" to bite (eg, mosquitos)... actually, wait... 'pico'
means "peak". Weird. So it's the same word, spelled differently, borrowed into English... fun.)