Ok I did it.
First, I had to create a
core.img that point to my drive explicity, Like this:
grub-mkimage --output=/tmp/core.img --prefix=\(hd3,1\)/boot/grub --format=i386-pc biosdisk part_msdos ext2
Second, I had to concatenate the lnxboot.img and core.img to create a image that can be booted by the boot sector application of the BCD Store.
cat /boot/lnxboot.img /tmp/core.img > /tmp/g2ldr
Third, I had to copy the g2ldr image to my windows partition and added to my BCD Store with a boot sector application.
Now I can boot Ubuntu from the boot manager of the BCD Store.