The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  2 2a+2 2a+2  0  2 2a+2  0  2 2a+2 2a 2a
 0  0  2 2a+2 2a+2  2 2a 2a  0 2a+2  2 2a  0  2

generates a code of length 14 over GR(16,4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+33x^40+192x^42+24x^44+3x^48+3x^56

The gray image is a code over GF(4) with n=56, k=4 and d=40.
This code was found by Heurico 1.16 in -3.24e-008 seconds.