  The Castelnuovo-Mumford polynomial $\widehat{\mathfrak{G}}_w$ with $w \in
S_n$ is the highest homogeneous component of the Grothendieck polynomial
$\mathfrak{G}_w$. Pechenik, Speyer and Weigandt define a statistic
$\mathsf{rajcode}(\cdot)$ on $S_n$ that gives the leading monomial of
$\widehat{\mathfrak{G}}_w$. We introduce a statistic $\mathsf{rajcode}(\cdot)$
on any diagram $D$ through a combinatorial construction ``snow diagram'' that
augments and decorates $D$. When $D$ is the Rothe diagram of a permutation $w$,
$\mathsf{rajcode}(D)$ agrees with the aforementioned $\mathsf{rajcode}(w)$.
When $D$ is the key diagram of a weak composition $\alpha$,
$\mathsf{rajcode}(D)$ yields the leading monomial of
$\widehat{\mathfrak{L}}_\alpha$, the highest homogeneous component of the
Lascoux polynomials $\mathfrak{L}_\alpha$. We use
$\widehat{\mathfrak{L}}_\alpha$ to construct a basis of $\widehat{V}_n$, the
span of $\widehat{\mathfrak{G}}_w$ with $w \in S_n$. Then we show
$\widehat{V}_n$ gives a natural algebraic interpretation of a classical
$q$-analogue of Bell numbers.
