use awk. For example to filter the reads having bases 1-5 = "TCTCT"

gunzip -c your.fastq.gz | paste - - - - |\
awk -F '\t'  '(substr($2,1,5)=="TCTCT")' |\
tr "\t" "\n"

Expanding Pierre's answer... You might want to check which are the most represented indexes in, say, the first 100000 reads:

zcat reads.fq.gz \
| head -n 100000 \
| paste  - - - - \
| awk '{idx=substr($2, 5, 5); print idx}' \
| sort \
| uniq -c \
| sort -k1,1nr

Remove the last three lines if you just want to see the indexes of each read.

Using grep before and after switches.

# extracts reads.
zcat reads.fq.gz | grep -A 2 -B 1 "^NNNNTCTCTC" > reads_out.txt
# count number of matches
zcat reads.fq.gz | grep "^NNNNTCTCTC" | wc -l