How to Design Nonlinear Phase FIR Filter?
Although not a comprehensive list, the following are filter algorithms available in Matlab for designing non-linear phase FIR filters:

firlpnorm: Nonlinear phase equiripple or least squares, uses Lp norm: for equiripple filters p = infinity, for least squares p =2.

cfirmpm: complex and nonlinear phase equiripple filters.

See the Matlab documentation for full details on how to design non-linear phase using these algorithms.