If the Last Will & Testament document itself is made public record by the Probate Court, the codicil should also be made public as well, in typical circumstances.
That being stated, there may be state or local rules of the court that prevent certain documents from being made public.
If you have questions about the Probate process in your location and the decisions of the Probate Court, you should consult with a local attorney on the matter. To find a local attorney for FREE, visit Standard Legal’s Attorney Find page.