There are several videos out on YouTube where people talk about intelligent design and there are some specific videos which address the question - "Is the brain Intelligently designed?" I think there are several ways to respond to this question. But first I will choose to look specifically at the phrase “intelligently designed.”
The word intelligence implies that some sort of agent has, what we would call, some thinking ability. This agent would have the ability to observe things and then gather that information and process it in such a way as to come to a conclusion about what is taking place.This agent would also have the ability to put in place it's own action to affect something external to itself. This agent would then need the ability to determine what design, if any, that would be required to effect some result and that design would hopefully be optimal for the task at hand.
Further the question "Is the brain intelligently designed?" is a begging question in that it is designed to elicit the response that yes the brain is intelligently designed and therefore some external agent is responsible for its design and that agent, to creationists, is God.
The second part of the question about design needs closer examination also. The implication from creationists is that design of something can't happen by itself, that some agent external to it must have caused design. However if one looks at our world we can see many examples of design in nature that are caused, not an intelligent agent, but by natural forces. The formation of river deltas by flowing water, the creation of various sand dunes by various winds, the design of shorelines interacting with rocks and sand, are examples of natural forces at work creating something that appears to have a design.
Our brain and the brains of animals, is the result of millions of years of evolutionary work that, through adaptation, came about to fulfill a task. Was it the best? No but it was good enough to accomplish what was needed to survive. If one looks at the human body as a whole it is not certainly the ideal creation, what with redundant and useless parts, with limitations in what the body can do and not do and so on. But it met the goal of surviving long enough to produce off springs that can tune the process for the next generation. And that's the goal of evolution. Live long enough to reproduce and then die.
It’s not what creationists want to hear but that’s the cold hard truth. We are not the end all of a supernatural being’s action for his/her/its benefit. We are here because events were such that we survived long enough to get to this state. Why weren’t we like this millions of years ago? Who knows? Maybe circumstances were such that some evolutionary process did not advance to the point that a particular creature could survive long enough to reproduce and continue the process. But then again maybe another creature did adapt in some small way and lived long enough to produce progeny. In the process these creatures improved in some evolutionary aspect and survived long enough to pass on those traits to more progeny. In time creatures changed, adapted and reproduced. Some made it, some didn’t. There are millions of dead ends in the course of evolution on the Earth and we are lucky, at this time, to have made it this far.
Think about it.