You aren't far off, but there are some errors. Excuse in advance any errors below, it's been a while since I did this stuff daily.
Human genome is 23 chromosomes, 2 copies of each (46). They are not mirror copies like RAID1, but rather alleles (different versions of same gene). So you might have a different version of a gene on each half of the chromosome. This is the basis for sexual selection and why sexual organisms can evolve (esp at the population level) so much faster than asexual ones. The two alleles can be the same as well. It's called homozygous or heterozygous. This is basic Mendelian genetics. Most genes work this way, though many are more complex.
ATGC is correct, so each "bit" is base 4.
Genes encode proteins; every 3 base pairs is a codon which specifies which Amino Acid to use. While there could be 4^3=64 in practice there are only 20 amino acids used in nature to make functional proteins. Genes vary greatly in length, not sure where you got ~200 codons/gene but that's terribly wrong. Maybe close to average, but the range is large. In any case, for data storage, anything relating to codons and proteins would be irrelevant.
Also in practice not all of a chromosome encodes proteins. There is often lots of buffer region between genes, not to mention a lot of control flow sequences that help control expression of genes. Beyond that, the ends of chromosomes don't have many genes, they just contain pseudo-random information and are still being explored (junk dna, telomeres, etc).