The generator matrix

 1  0  1  1  1  1  1  1  1  2  1  1  1  1
 0  1 2a+3  a a+1  2 2a+1 a+2 a+3  1 2a  3 3a 2a+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+51x^40+72x^41+48x^42+54x^44+24x^45+6x^48

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 0 seconds.