Fermat quartic/Syz (x,y,z)/Characteristic 3/Semistable, not strongly semistable/Example

Let ${}C$ be the smooth Fermat quartic given by ${}x^{4}+y^{4}+z^{4}$, and consider on it the syzygy bundle ${}\operatorname {Syz} {\left(x,y,z\right)}$ (which is also the restricted cotangent bundle from the projective plane). This bundle is semistable. Suppose that the characteristic is ${}3$. Then its Frobenius pull-back is ${}\operatorname {Syz} {\left(x^{3},y^{3},z^{3}\right)}$. The curve equation gives a global non-trivial section of this bundle of total degree ${}4$. But the degree of ${}\operatorname {Syz} {\left(x^{3},y^{3},z^{3}\right)}(4)$ is negative, hence it can not be semistable anymore.