Can random mutations cause an increase in information in the genome?

In terms of mutations, the entire process is clearly not so random as evos have suggested, and in fact, may not even be random at all since we really have no way to know, as far as science, what the Intelligent Cause of the universe planned and knew about evolution, except that it is logical to consider that an Intelligence that advanced could predict what would occur with considerable accuracy, and perhaps even governs what occurs moment to moment.