And if it is a "very-well-behaved" one (no such sequence in any header, then a fixed word search would be even slightly faster ;)
grep -B1 -A2 -F -w AACTACGTCCATC test.fq
Edit: just tested on a very large fastq file and the -w option is not at all faster than a proper start-end search. grep -B1 -A2 "^AACTACGTCCATC$" test.fq is definitely faster.
"not as part of a longer sequence" is exactly the opposite of "even though its withing a longer sequence". Maybe you should clarify that, although it looks like a simple grep would do.