Phukie,
Your derivation of the logic function is flawed. The correct equation is shown below. Once you figure out the correct logic equation, you can use the program I wrote in the attachment below to get the minterms. Make sure you read the program instructions carefully. Then use a Karnaugh map (K-map) and plug in the minterms to get the best reduction. Afterwards, by the method shown in any logic book, you can also change the logic gate functions to see what gives you the least parts count, least cost, simplest circuit, etc. According to the K-map, the logic function reduces to C+D' .
This is the logic function of your problem (AB')'(B'C)(C+D)+C(C+D+D)+D' where ' means "not". You should confirm its correctness and learn how to do it yourself.
Ratch