Classification of DNA Sequences
One way would be to create 20 features (each feature representing a codon). In this way, you would have a dataset with 3190 instances and 20 categorical features. There is no need to treat the sequence as a Markov chain. 

Once the dataset has been featurized as suggested above, any supervised classifier can work well. I would suggest using a gradient boosting machine as it might be better suited to handle categorical features.