A problem formulation which I modified slightly can be found in [frutos1997demonstration]. This reference also describes the construction of a solution of size 108.
[DBLP:conf/ijcai/Codish0L17]
The DNA Word Design Problem: A New Constraint Model and New Results
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, {IJCAI} 2017, Melbourne, Australia, August 19-25, 2017, 585–591,
2017
[tulpan2006effective]
Effective heuristic methods for DNA strand design
Ph.D. thesis, University of British Columbia
2006
[frutos1997demonstration]
Demonstration of a word design strategy for DNA computing on surfaces
Nucleic Acids Research 25(23), 4748–4757,
1997