How can I make an image fit into available space when too wide?

I have an image asset which is 1250px wide. I want it to fill the given space, but because the image is too large I always get an overflow error. I have tried specifying a width for the image, but of course this is device dependent so is not a solution. How can I make this fit into the given space?

Widget build(BuildContext context) {
    return Stack(
      children: [
        Column(
          children: <Widget>[
            Padding(
              padding: EdgeInsets.only(
                  left: 12.0, top: 5.0, bottom: 16.0, right: 0.0),
              child: Row(
                children: [
                  Image.asset(
                    'assets/images/my_image.png',
                    fit: BoxFit.fitWidth,
                    width: 348, // works on one device but not others
                  ),
                ],
              ),
            ),
          ],
        ),
      ],
    );
  }