A check of the GLIMMIX documentation (see the Syntax section for the MODEL statement) shows that the default link for the multinomial distribution is the cumulative logit, which causes response outcomes to be ordered. See the "Response-Level Ordering and Referencing" section in the GLIMMIX documentation for a description of default ordering and how to change it, if need be.
For unordered response outcomes, you'll want to use the generalized logit link (again, see the Syntax section for the MODEL statement).
Since you're a new SAS user, I'll point out that you do not need to code dummy variables for categorical predictors in any SAS procedure that has a CLASS statement, unless you need to for some specific reason. Using the CLASS statement and the implicit tests and estimates that are embedded in the procedure is easier and less error-prone than devising your own ESTIMATE and CONTRAST statements.