The generator matrix

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

generates a code of length 29 over GR(16,4) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+156x^77+372x^78+312x^79+438x^80+1260x^81+1152x^82+528x^83+372x^84+1764x^85+1368x^86+576x^87+396x^88+2436x^89+1728x^90+624x^91+402x^92+1296x^93+756x^94+264x^95+156x^96+12x^100+6x^104+6x^108+3x^112

The gray image is a code over GF(4) with n=116, k=7 and d=77.
This code was found by Heurico 1.16 in 57.5 seconds.