Minimal dimension conjecture for Malcev algebras of the second type

A Malcev algebra of the first type is an anticommutative algebra satisfying

$$J(xy,z,u)+J(yz,x,u)+J(zx,y,u)=0,$$

and

$$J(x,y,uv)=J(x,y,u)v-J(x,y,v)u,$$

where $J(x,y,z)=(xy)z+(yz)x+(zx)y$. A Malcev algebra of the second type satisfies

$$J(x,y,z)x=J(x,y,xz)=0.$$

Minimal dimension conjecture. Every Malcev algebra of the second type of dimension $<23$ over a field of characteristic $0$ is an algebra of the first type.