Messages like:
Network Shield: blocked "DCOM Exploit" - attack from 81.178.115.162:135/tcp
are due to the RPC/DCOM exploit, which is a vulnerability that allows an attacker to gain access to the destination machine by sending a malformed packet to the DCOM service. It uses the RPC TCP port 135.
DCOM Attacks are speculative, not targeted and tries to exploit a vulnerability in out of date OS, if your OS is up to date then you aren't vulnerable to the exploit. That doesn't stop them (usually someone from the same ISP with an infected computer) trying to see if it can infect others.
Your firewall should be the first line of defense in this, but avast also monitors common attack ports using the Network Shield, ideally the firewall should block it and avast wouldn't know about it, but for whatever reason avast is first in line over your firewall.