Is there a $\triangle ABC$, with $D$ inside, such that $AB$, $BC$, $CA$, $AD$, $BD$, $CD$ are all integers, but only one is even?

Question

This was another problem given to me by one of my math teachers that I don’t know how to solve.

Here it is:

We have a triangle $ABC$ and point $D$ is inside the triangle. Is it possible to assign integer lengths to $AB$, $BC$, $AC$, $AD$, $BD$, and $CD$, such that only one of these lengths has an even value? If it is possible what are the lengths and their configuration?

(I recently asked a separate question where $D$ is taken to be on side $BC$.)

I don’t have much work for this problem. I tried to isolate quadrilateral $ABCD$ from side $AC$ to try to use Euler’s quadrilateral theorem on $ABCD$, however I am unsure if this will work. This is because $ABCD$ is a concave quadrilateral and I don´t recall reading anywhere that Euler’s Quadrilateral Theorem works on concave quadrilaterals.

Other than this, I don’t have any ideas to solve this problem, so please help.