  Let $k$ be a field of characteristic zero and $R$ a $k$-algebra. In this
paper we study homogeneous $R$-lnds $D$ on $R[X,Y,Z]$ with respect to the
standard weights $(1,1,1)$. We show that when $R$ is a PID, $rank(D)$ can be at
most $2$ if $\deg(D) \leqslant 3$. As a consequence we obtain a certain class
of homogeneous lnds on $k^{[4]}$ whose kernel is $k^{[3]}$. Further when $R$ is
a Dedekind domain, we give a bound for minimum number of generators of
$\ker(D)$ as an $R$-algebra if $\deg(D) \leqslant 3$.
