The size of the complete matrix not withstanding, 304805 letters is not a huge dataset. Informatics approaches exist for identifying relationships in much larger datasets. You are probably going to need to 1) find ways to identify and eliminate non-informative subsets of the matrix, or 2) render subsets of the matrix on the fly if you want a purely visual analysis approach.
PDL can manage objects of about 500x500x500 with <1GB of RAM using doubles for coordinates. If plain dots won't work for you, I'm not certain how you would go about rendering suitable glyphs.
If you're willing to go outside perl you may also find some benefit from systems like
Good luck with the project.