Existence of a nonrepetitive palindrome-free sequence avoiding two subsequences

Let an infinite sequence be a sequence whose terms are drawn from the four-letter alphabet $\{A,B,C,D\}$. A sequence is nonrepetitive if it contains no contiguous block of the form $XX$ for a nonempty finite word $X$, and palindrome-free if it contains no nonempty palindromic contiguous block. It avoids the subsequences $CD$ and $DC$ if neither of these occurs as a subsequence.

Sequence existence conjecture. There exists an infinite sequence on four letters, $A,B,C$ and $D$ such that the sequence is nonrepetitive, palindrome-free and avoids the subsequences $CD$ and $DC$.

The paper states that this conjecture was recently confirmed by Kozik, so the existence claim is resolved.