DA20 student pilot; on his first solo cross country; reports getting lost and requesting assistance from approach control. Poor visibility was reported as a factor.

Narrative

I took off in the morning on my first solo cross country. The visibility was bad; but enough for to flight. My first destination 20 miles from my first destination the visibility was very bad. I landed at the first aircraft. I did a take off and looked for my second destination but I do not see the ground so good. I was lost. It was getting late. I saw an airport and I thought it was my destination. I flew to this airport and then I saw the runway numbers. I read 29; but my destination had 24. In this moment; I know; you were on the wrong airport and you were lost. I called with my destination Tower and asked him for a heading to the airport; because I could not find it. The man said; he could not help me and he gave me the frequency for Approach. I called to Approach and explained him my situation. He gave me a squawk code; a heading for my destination airport; and an altitude. He gave me a phone number; and I called to this number as soon as I landed at my destination. I landed at my destination and waited of my flight instructor. He flew to the airport and then together back to home field.