The generator matrix

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

generates a code of length 15 over GR(16,4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+93x^28+246x^32+360x^36+579x^40+852x^44+12288x^45+945x^48+636x^52+309x^56+75x^60

The gray image is a code over GF(4) with n=60, k=7 and d=28.
This code was found by Heurico 1.16 in 0.293 seconds.