Dog80: The examples you’ve given are probably not the most appropriate. Eye color, for example, is determined by a fairly well-understood set of genes. Same with skin color, hair color, etc. Something like height is indirectly genetic – there are genes for growth hormones (and for all the machinery necessary for growth), and there are other genes that regulate the growth genes. The regulatory genes determine how much growth hormones are produced, so different people will produce different amounts of the hormones, and grow to different heights. (There are other factors, such as nutrition.)
Perhaps what you mean is that there is not enough information stored in DNA to explain things like, say, intelligence, or compassion. These sorts of things are partly genetic, but also depend on cultural and other external factors. Structural information, such as the shape of the hand, is not well-understood now. There are genes (e.g. Sonic hedgehog) that determine limb structure, but the details are not certain. It is possible that the vast amount of introns, or ‘junk’ DNA that does not code for proteins, contain some of the ‘missing’ information. (Most junk DNA, however, probably just protects the important stuff.)
The idea that the human genome doesn’t have enough information to fully explain humans probably results from our currently patchy understanding of human genetics. We know a lot about the genes that produce catalytic proteins, less about the genes that regulate those genes, and less still about the part of DNA that does things like determine the structure of the body or brain. It is not necessary to invoke magic or the supernatural to explain how roughly 3 billion base pairs, or 30,000 genes, can produce a human.