Example of the matrix of size $6\times6$ with different tropical rank and Kapranov rank

We provide an example of a $6$-by-$6$ matrix $A$ such that $\operatorname{rk}_t(A)=4$, $\operatorname{rk}_K(A)=5$. This disproves the conjecture formulated by M. Chan, A. Jensen, and E. Rubei.