In this question, the word "as" introduces a comparison, and our primary task is to express the comparison accurately.
Choice (A) uses the pronoun "that" to refer to "study." It's saying, in other words, that the study of computer code is as important as "[the study] of the written word." The pronoun "that" has a clear reference, and the comparison is logical--it's between one study and another study. Choice (A), therefore, is accurate.
Choice (B), as written, compares a "study," that of computer code, to "the written word," so it makes an illogical comparison.
Choice (C) distorts the meaning of the sentence. As written, it says simply that both studies are important but doesn't compare them, as the original is clearly intended to do.
Choice (D) is somewhat awkward and inaccurate. Comparisons require parallel structure, so we should compare the "study of" one thing to the "study of" another thing. On these grounds, we eliminate choice (D), and also choice (E).
The correct answer is (A).