Is it possible to find a nash equilibrium that is not an equilibrium in weakly dominant strategy?

begin{array}{|c|c|c|} hline &L&Rhline T&1,1&0,0hline B&0,0&0,0hline end{array}

In the game above, there are two pure strategy Nash equilibria:

• $(T,L)$ is an equilibrium in weakly dominant strategies;
• $(B,R)$ is an equilibrium in weakly dominated strategies.

Noting that "dominant" and "dominated" are two different words, I believe the above example answers both the question in your post as well as your question in the comment below.