The generator matrix

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

generates a code of length 30 over GR(16,4) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+444x^78+984x^79+1062x^80+660x^81+1788x^82+2388x^83+2085x^84+1452x^85+3972x^86+4884x^87+3963x^88+2916x^89+6420x^90+6972x^91+4287x^92+3300x^93+5808x^94+5316x^95+3015x^96+888x^97+1536x^98+960x^99+411x^100+15x^104+9x^108

The gray image is a code over GF(4) with n=120, k=8 and d=78.
This code was found by Heurico 1.16 in 64.9 seconds.