Replicated the problem (Active Perl 5.8.8, WinXP) and it's definitely a bug.

The code does get executed. Changing
my $code2='$string="new eval done";';
to
my $code2='$string="new eval done"; print "!"';
prints an exclamation point. Perl just doesn't seem to access $string properly.

The bug doesn't manifest itself if you change
my $code1='my $var_with_é_accent;';
to
my $code1='$var_with_é_accent;';

By the way, that's a iso-latin-1 encoded é, "\xE9".