The generator matrix

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

generates a code of length 15 over GR(16,4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+45x^44+192x^45+15x^48+3x^60

The gray image is a code over GF(4) with n=60, k=4 and d=44.
This code was found by Heurico 1.16 in 3.24e-008 seconds.