Yes it is possible and artificial DNA called XNA (xeno-nucleic acid) has already been created. DNA is made of by stringing nucleotides together. A nucleotide contains a nucleobase (A, C, T or G), a sugar group and a phosphate. XNA has been created by replacing the sugar group. Normally in DNA the sugar group consists of 5 carbons, in XDA this sugars can be made from 4-7 carbons. Like DNA, XNA can make copies of themselves, and by creating new enzymes, scientists have been able to convert DNA into XNA, and back again.