fixing the mail permission as Think Support suggested.
Result from tail:
tail -f /var/log/exim_mainlog|grep -i xxxx.com
2005-11-18 19:02:20 1Ed40a-0002dh-0x <=
lxxxx@xxxx.com U=xxxx P=local S=575
2005-11-18 19:03:42 1Ed41t-0002lQ-Tf => :blackhole: <xxxx@xxxx.com> R=virtual_aliases
2005-11-18 19:06:33 1Ed44f-0002wG-TY <=
xxx@xxxx.com U=xxxx P=local S=585
2005-11-18 19:06:59 1Ed455-0002wo-H6 => :blackhole: <xxxx@xxxx.com> R=virtual_aliases
I've realize that i can email from external mail address but not from the domain from my server