Weight-enumerator conjecture for the Kassami APN design code

Let $n\geq5$ be odd. Let $\mathsf{C}_2(\mathbb{KA}_{n,1})$ denote the binary linear code generated by the block characteristic vectors of $\mathbb{KA}_{n,1}$. Kassami-code parameter conjecture. The code has parameters

$$[2^n,2n+1,2^{n-1}-2^{(n-1)/2}]$$

and weight enumerator $1+uz^{2^{n-1}-2^{(n-1)/2}}+vz^{2^{n-1}}+uz^{2^{n-1}+2^{(n-1)/2}}+z^{2^n}$, where $u=2^{2n-1}-2^{n-1}$ and $v=2^{2n}+2^n-2$. Its dual has parameters

$$[2^n,2^n-2n-1,6].$$

The source presents this as an unverified conjecture; no general resolution is supplied.