The generator matrix

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

generates a code of length 12 over GR(16,4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+330x^24+396x^28+495x^32+13608x^36+990x^40+396x^44+168x^48

The gray image is a code over GF(4) with n=48, k=7 and d=24.
This code was found by Heurico 1.16 in 0.228 seconds.