First some house keeping: excellent to see you using strictures, however -w in the shebang line isn't needed because you are using use warnings. Actually -w has global effect (it applies to code outside the current file) whereas use warnings only applies to the current file and is preferred.

Next item of house keeping: use indentation to show structure. The code in your sub should be indented.

Final house keeping hint: make returned values explicit. return <<"END_MSG"; instead of <<"END_MSG";.

To figure out where white space is it helps to add "quote" characters. Try:

#!/usr/bin/perl
use strict;
use warnings;

sub foo {
    my $code = shift;

    return <<"END_MSG";
Add the code
<$code>
END_MSG
}

my $code = <<'END_MSG';
line 1
line2
END_MSG

print "before calling\n";
print $code;

print "after calling\n";
print foo($code);

print "why blank line above?\n";
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and you will see that the contents of $code already has a trailing newline so nesting it in another HEREDOC adds the second unwanted newline. One fix is to chomp $code in the sub:

sub foo {
    my $code = shift;

    chomp $code;
    return <<"END_MSG";
Add the code
$code
END_MSG
}
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