We introduce the problem of polyomino Gray codes, which is the listing of all members of certain classes of polyominoes such that successive polyominoes differ by some well-defined closeness condition (e.g., the movement of one cell). We discuss various closeness conditions and provide several Gray codes for the class of column-convex polyominoes with a fixed number of cells in each column. For one of our closeness conditions, a natural new class of distributive lattice arises: the partial order is defined on the set of m -tuples [ S 1 ] × [ S 2 ] × ⋯ × [ S m ] , where each S i > 1 and [ S i ] = { 0 , 1 , … , S i − 1 } , and the cover relations are ( p 1 , p 2 , … , p m ) ≺ ( p 1 + 1 , p 2 , … , p m ) and ( p 1 , p 2 , … , p j , p j + 1 , … , p m ) ≺ ( p 1 , p 2 , … , p j − 1 , p j + 1 + 1 , … , p m ) . We also discuss some properties of this lattice.