14. Danika drove her new car for an integer number of hours, with the car averaging 55 miles per hour. At the start, the odometer read $\overline{a b c}$, where $\overline{a b c}(a \geqslant 1, a+b+c \leqslant 7)$ is a three-digit number, and when she stopped, the odometer read $\overline{c b a}$. Then $a^{2}+b^{2}+c^{2}=$ ( ).
(A) 26
(B) 27
(C) 36
(D) 37
(E) 41
14. D.

Let Danyika drove for $n\left(n \in \mathbf{Z}_{+}\right)$ hours.
From the problem, we have
$$
\begin{array}{l}
100 a+10 b+c+55 n=100 c+10 b+a \\
\Rightarrow 9(c-a)=5 n .
\end{array}
$$

Since $(5,9)=1$, it follows that, 5 divides $(c-a)$.
Thus, $(a, c ; n)$
$$
=(1,6,9),(2,7,9),(3,8,9),(4,9,9) \text {. }
$$

Also, $a+b+c \leqslant 7$, so,
$$
(a, b, c, n)=(1,0,6,9) \text {. }
$$

Therefore, $a^{2}+b^{2}+c^{2}=1+0+36=37$.