Bonanza pilot reported after receiving an IFR climb clearance while airborne they descended to avoid weather and received a low altitude warning from ATC.

Narrative

Filed an IFR for flight plan to ZZZ1 for thirteen thousand feet. Departed ZZZ and headed north and noticed a line of thunderstorms quickly forming ahead of me. I called ZZZ Approach after take off and they gave me a squawk code and they said maintain VFR. I called back and said I needed to amend to eleven thousand feet and needed to maneuver around these storms right ahead of me. I believe I was stepped on and he didn't hear me. Approach radioed back to go direct ZZZZZ (or on course) and climb to ten thousand. I radioed back; I need to stay below two thousand to avoid the build up ahead of me. I believe I was stepped on again and he did not hear me. I then descended to get below the weather and went below the weather to about 1500 feet. Approach Control called back saying that I'm low. I replied back that I'm trying to avoid a storm and believe I was stepped on again. I safely maneuvered through the weather and began my climb and reached out to Approach Control to let him know that I was continuing on course and climbing to ten thousand. He asked me sky conditions and I said fine after going through the line of thunderstorms. There were no other issues after that. With Approach transmitting on two different frequencies and the increase of civilian and military traffic in the area it makes it difficult for clear communications.