The generator matrix

 1  0  1  1  1  1  1  2  1  1  1 2a  1  1  1
 0  1 2a+3  a  2 2a+1 a+2  1 2a  3 3a  1 2a+2  1 3a+2

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.