open(FILE, 'file') || die("Yaroo!\n");
my $N = 3; # 3 lines above and below
my $target = 'stuff what you want';
my @window = ('') x ($N + $N + 1);
while(<FILE>) {
    shift @window;
    push @window, $_;
    print @window, "\n\n" if($window[$N] =~ /$target/);
}
foreach(1 .. $N) {
    shift @window;
    print @window, "\n\n" if($window[$N] =~ /$target/);
}