On finding certain minimal generating set of the maximal ideal in a local ring of positive depth

Question

Let $(R,\mathfrak m)$ be a local ring with depth $R=2$ and $\mu(\mathfrak m)=4$. Then, does there exist $x_1,x_2, x_3, x_3\in \mathfrak m$ such that $\mathfrak m=(x_1,x_2,x_3,x_4)$ and $x_i,x_j$ is an $R$-regular sequence for every $i<j$ ?