You can say straightly: "Wǒ kāi de hěnmàn." You don't have to say: "kāichē", becouse when you say "kāi" the people will see that means "kāichē".
This scentence's grammer is about the "complement of state", usually,the structure is Verb + de(得)+adjective. The word after "de(得)" is a comlement which expresses the state. "hěnmàn"is a comlement here and it expresses the state of "kāi".
If you have to use "kāichē", you should say:"Wǒ kāichē kāi de hěnmàn."
Example sentence: "Tā pǎo de hěnkuài. (he runed very fast.)"; or you can say:"Tā pǎobù pǎo de hěnkuài."