You just add SOLUTION in the RANDOM statement in which you specify your random effects as in any PROCMIXED worksheet. The fixed effects are specified in the MODEL statement. 

A good review has been made of Piepho et al 2008 titled "BLUP for phenotypic selection in plant breeding and variety testing". It throws light on to whether to use genotypes as fixed or random effects.

However, I used blocks and genotypes as random effects while checks as fixed effects in proc mixed.

In case anyone is wondering what a BLUP is - it is the estimated shrunken random effect where the degree of shrinkage towards zero depends on the degree of (im)precision of the estimate

I have put this paper (in a very different context to the original question) on RGate - it has plenty of references to the  literature on this type of estimate

https://www.researchgate.net/publication/266383638_A_model-_based_approach_to_the_analysis_of_a_large_table_of_counts_occupational_class_patterns_in_among_Australians_by_ancestry_generation_and_age_group

This (still) unfinished paper makes the link to classical measurement error

https://www.researchgate.net/publication/252146040_Do_multilevel_models_ever_give_different_results

Article A model- based approach to the analysis of a large table of ...

Article Do multilevel models ever give different results?.

The problem is more directed to statistical modelling than SAS PROC MIXED use. In short, SAS PROC MIXED could design the effect as fixed or random, and is have some flexibility to eval some complex models. The user need to define the model. In this point I could ask about the effects and variabels in Your model. Could You share it?