Bricks are polyominoes with labelled cells. The problem whether a given set of bricks is a code,is undecidable in general. It is open for two-element sets. Here we consider sets consisting of square bricks only. We show that in this setting,the codicity of small sets (two bricks) is decidable, but15 bricks are enough to make the problem undecidable. Thus the frontier between decidability and undecidability lies somewhere between these twonumbers. Additionally we show that the undecidability frontier could be improved to 13 if the Post Correspondence Problem with three pairs should prove undecidable.