Enumeration of strictly Deza graphs with at most $21$ vertices

A Deza graph $\Gamma$ with parameters $(v,k,b,a)$ is a $k$-regular graph with $v$ vertices such that any two distinct vertices have $b$ or $a$ common neighbours, where $b \geqslant a$. A Deza graph of diameter $2$ which is not a strongly regular graph is called a strictly Deza graph. We find all $139$ strictly Deza graphs up to $21$ vertices and list corresponding constructions and properties.