This is an English usage question more than one of biology. The verb code has two main meanings(1):
- (transitive) to put into the symbols of a code
- (intransitive) to be a code symbol
The first, which being transitive takes an object, is used for the act (as by a person) of translating a plain message into a corresponding encoded form. This is not the meaning used in "AAG codes for lysine".
The second form does not take an object. It is not being done to something, but rather is just a state of being. This form is almost always followed by a prepositional phrase "for noun", as in "INS codes for insulin".
Hence it is not correct English to say things like "INS codes insulin", as the use of "insulin" as an object implies the first meaning, as if one were saying "INS takes an insulin molecule and puts it into an encoded form" (whatever that would mean).
The reader would likely try to interpret "INS codes insulin" with the intended meaning, but the incorrect usage makes it seem equivalent to something like "INS is a DNA sequence insulin." Leaving out the preposition for may be shorter, but it gives a bumpier ride.
(1): Merriam-Webster. For more variants see Wiktionary, esp. encode.