Kg7 is mate in 6 at best I think. Basically any move black takes it's gonna be mate in less than 10 unless you start blundering pieces.

1. a7 Qe5
2. Bxe7 Qe7
3. Bxf6+ Qe5
4. Rxf4#

I think that's valid? Also

1. a7 Qe5
2. Bxe7 axb1=Q
3. d8=Q+ Qd5
4. Qxd5#

But there's still

1. a7 Qd6
2. crap