Internal container cannot reach Internet
Supposing you have connectivity to other addresses of the host, probably you need to set up some kind of NAT.
There is plenty of ways to do it, (check links in the references). One that requires little asumptions about the case is to MASQUERADE the packets with iptables.
In this case the "NATed" network is 10.0.4.0/24:
iptables -t nat -A POSTROUTING -s 10.0.4.0/24 '!' -d 10.0.4.0/24 -j MASQUERADE