What is an example of a $3$ dimensional smooth distribution $D$ of $\mathbb{R}^4$ with the property quoted bellow?

Not only $D$ is not integrable but also there is no a $2$ dimensional foliation $F$ of $\mathbb{R}^4$ such that for every $x\in \mathbb{R}^4$, the tangent space to each leaf at $x$ is contained in $D_x$?

What is an example of a three-dimensional smooth distribution $D$ of $\mathbb{R}^4$ with this property:

Not only $D$ is not integrable but also there is no a two-dimensional foliation $F$ of $\mathbb{R}^4$ such that for every $x\in \mathbb{R}^4$, the tangent space to each leaf at $x$ is contained in $D_x$.

What is an example of a $3$ dimensional smooth distribution $D$ of $\mathbb{R}^4$ with the property quoted bellow?

Not only $D$ is non integrable but also there is no a $2$ dimensional foliation $F$ such that for every $x\in \mathbb{R}^4$, the tangent space to each leaf at $x$ is contained in $D_x$?

What is an example of a $3$ dimensional smooth distribution $D$ of $\mathbb{R}^4$ with the property quoted bellow?

Not only $D$ is not integrable but also there is no a $2$ dimensional foliation $F$ of $\mathbb{R}^4$ such that for every $x\in \mathbb{R}^4$, the tangent space to each leaf at $x$ is contained in $D_x$?