For placement of the regex switches, see How do I apply switches like /i or /g to a qr regexp?:

/imsx immediately follow the closing delimiter of the qr, but /gce must be supplied at the point of actual use immediately following m// or s///.

Hope that helps,

Thank you very much Athanasius!

... speed up the regex:
my $regex = qr/p[^x]+l/;

Please be aware that use of the  /i case-insensitivity regex modifier usually imposes a speed penalty, perhaps quite significant if you're really dealing with long-ish (e.g., DNA) strings. Using a character class avoids this:
    my $regex = qr/[Pp][^x]*[Ll]/;
with no  /i modifier needed anywhere. As always, Benchmark-ing tells the true tale with regard to performance in a real application; anything else, however well informed, is speculation.

Also be aware that the  [^x]+ term in the quoted regex requires at least one non-'x' to be present for a match, thus excluding a match on something like 'pl'. So the final code might look like the following code. (Note that  () capturing parentheses are not needed in this case and may impose a speed penalty.)

>perl -wMstrict -le
"my $dna = 'xxpecbcbccrlxxxPeeeerlxxpLxxxPeRLxx';
 ;;
 my $perl = qr{ [Pp] [^x]* [Ll] }xms;
 ;;
 my @matches = $dna =~ m{ $perl }xmsg;
 printf qq{'$_' } for @matches;
"
'pecbcbccrl' 'Peeeerl' 'pL' 'PeRL'
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