The generator matrix

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

generates a code of length 28 over GR(16,4) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+372x^78+348x^79+435x^80+240x^81+564x^82+324x^83+258x^84+60x^86+324x^87+204x^88+144x^89+540x^90+156x^91+126x^92

The gray image is a code over GF(4) with n=112, k=6 and d=78.
This code was found by Heurico 1.16 in 0.75 seconds.