What could I do to improve it’s power?
Increase the number of turns.
The strength of the magnetic field produced by an electromagnet is approximately proportional to the current through the coil X the number of turns in the coil.
The resistance of the electromagnet is approximately proportional to the length of the wire divided by the diameter of the wire squared.
The current through the coil is equal to the voltage applied across the coil divided by the resistance of the coil.
When a thicker wire is used in a multilayer coil, the same number of turns will require a longer wire. Turns near the center of a coil are not as long as turns on the outside. The thicker the wire, the larger the "outside" turns be, and the longer the wire needed to make them.
Increasing the length of wire used without changing the wire diameter will increase the resistance, decrease the current, and increase the strength of the magnetic field per unit current, all by approximately the same factor. The change in the magnetic field will be modest, because although magnetic field per unit current will increase by some factor, the current will decrease by approximately the same factor. Although the change in magnetic field is modest, the power consumed by the coil will be reduced by approximately the ratio of the old wire length to the new wire length. Not only does this save on batteries, but it allows the coil to run cooler.
Increasing the length of wire by a given factor \$k\$, while simultaneously increasing the wire diameter by a factor of \$\sqrt{k}\$, will have the effect of approximately increasing the magnetic field strength by a factor of \$k\$, while leaving the power consumption and current very approximately constant (i.e. don't be surprised by non-trivial level of change).
Since the power supplied by your battery is limited, and is not free, to increase the magnetic strength by some multiples, you will need to both increase the length of wire used, and its diameter. Of course, wire is expensive, (and can also be heavy, and bulky) so there is a trade-off to be made there as well. How much is it worth it to you do double, triple or quadruple the magnetic strength? You must make the ultimate decision there.