The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+81x^24+240x^27+135x^28+576x^30+1008x^31+147x^32+3456x^34+1872x^35+222x^36+5184x^38+3024x^39+237x^40+171x^44+30x^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 0.12 seconds.