Perlin noise looks uncoherent on higher z

Question

I was experiencing with my Perlin noise function and I tried to animate a 2D noise by changing the z value of a small amount every frame. However, as z increases, the result becomes stranger and stranger, looking like this:

Why is this happening? How could I solve this?

Here's the Lua code that could be wrong (as asked):

function perlin.fade(t)
    return t * t * t * (t * (6 * t - 15) + 10)
end
function perlin.lerp(t, a, b)
    return a + t * (b - a)
end
function perlin.grad(hash, x, y, z)
    local h = hash % 16
    local u
    local v
    if (h < 8) then u = x else u = y end
    if (h < 4) then v = y elseif (h == 12 or h == 14) then v = x else v = z end
    local r
    if ((h % 2) == 0) then r = u else r = -u             end
    if ((h % 4) == 0) then r = r + v else r = r -v end
    return r
end
function perlin:noise(x, y, z)
    y, z = y or 0, z or 0
    local X = math.floor(x) % 256
    local Y = math.floor(y) % 256
    local Z = math.floor(z) % 256
    x = x - math.floor(x)
    y = y - math.floor(y)
    z = z - math.floor(z)
    local u = perlin.fade(x)
    local v = perlin.fade(y)
    local w = perlin.fade(z)
    local A  = self[X + 1] + Y
    local AA = self[A + 1] + Z
    local AB = self[A + 2] + Z
    local B  = self[X + 2] + Y
    local BA = self[B + 1] + Z
    local BB = self[B + 2] + Z
    return perlin.lerp(w, perlin.lerp(v, perlin.lerp(u, perlin.grad(self[AA + 1], x    , y    , z    ),
                               perlin.grad(self[BA + 1], x - 1, y    , z    )),
                       perlin.lerp(u, perlin.grad(self[AB + 1], x    , y - 1, z    ),
                               perlin.grad(self[BB + 1], x - 1, y - 1, z    ))),
               perlin.lerp(v, perlin.lerp(u, perlin.grad(self[AB + 2], x    , y    , z - 1),
                               perlin.grad(self[BA + 2], x - 1, y    , z - 1)),
                       perlin.lerp(u, perlin.grad(self[AB + 2], x    , y - 1, z - 1),
                               perlin.grad(self[BB + 2], x - 1, y - 1, z - 1))))
end

Answer 1

Here:

    perlin.lerp(v, perlin.lerp(u, perlin.grad(self[AB + 2], x    , y    , z - 1),

This should have AA + 2 instead.