Diophantine symmetric quadratic system

Take a box $ mathcal B subseteq mathbb Z ^ 8 $ around the origin of the same side lenth $ ell $. What is the minimum $ ell $ need for the following system quadratic polynomials to have a solution $ mathcal B $

$$ wz + xy = w & z; + x & # 39; y & # 39; = wz + xy & # 39; = w + x + y = 0 $$
with $ | wx | neq | yz | neq | w & # 39; x & # 39; neq | There & # 39; z & # 39; | $?