minimizing distance of the linear image of a vector of $\mathbb{Z}/2\mathbb{Z}$

Question

let $A \in M_ {m,n} (\mathbb{Z}/2\mathbb{Z})$ and $Q \in M_n (\mathbb{Z}/2\mathbb{Z})$ , is there a way to find $X \in M_n (\mathbb{Z}/2\mathbb{Z})$ minimizing $||AX+Q||$ where $||vector||$ mean the sum of the coordinate of the vector considered as $\mathbb{R}$ element ?