Here an other approach but I have a problem to repeat the following code 14 times:
\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-n) {\Alph{answer}}; from n=1 to n=14

\documentclass{article}
\usepackage{tikz}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\answergrid}{ m m m }{
\begin{tikzpicture}[x=.6cm, rotate=90]
\seq_set_split:Nnn \splitted_seq{;}{#3}
\newcounter{answer}
\int_step_inline:nnnn {1} {1} {#2} {
\stepcounter{answer}
%----> the problem!!!
\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-1) {\Alph{answer}};
\node[fill=green!10,minimum~width=6mm,minimum~height=4mm,] at (6-##1,#1-2) {\Alph{answer}};
\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-3) {\Alph{answer}};
\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-4) {\Alph{answer}};
\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-5) {\Alph{answer}};\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-6) {\Alph{answer}};\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-7) {\Alph{answer}};\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-8) {\Alph{answer}};\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-9) {\Alph{answer}};\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-10) {\Alph{answer}};\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-11) {\Alph{answer}};\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-12) {\Alph{answer}};\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-13) {\Alph{answer}};
\node[fill=green!10,minimum~width=6mm,minimum~height=4mm] at (6-##1,#1-14) {\Alph{answer}};}
\int_step_inline:nnnn {1} {1} {#1} {
\node[fill=black!50,text=white, minimum~width=6mm,minimum~height=4mm] at (6, #1-##1) {\bf ##1};
\int_step_inline:nnnn {1} {1} {#2} {
\int_compare:nNnTF {####1} = {\seq_item:Nn \splitted_seq {#1-##1+1}} {
\node[fill=red!10,draw,minimum~width=7mm,minimum~height=4mm] at (6-####1, ##1-1) {B};
}{
\node[draw=blue,minimum~width=7mm,minimum~height=4mm] at (6-####1, ##1-1) {};
}
}
}
\end{tikzpicture}
}
\ExplSyntaxOff
\begin{document}
\par
\answergrid {15} {5} {2;0;0;0;0;0;2;0;0;0;0;2;0;0;0;0;0}
\end{document}