The generator matrix

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

generates a code of length 29 over GR(16,4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+384x^81+192x^82+648x^83+144x^84+576x^85+336x^86+456x^87+12x^88+96x^90+216x^91+96x^92+576x^93+144x^94+216x^95+3x^96

The gray image is a code over GF(4) with n=116, k=6 and d=81.
This code was found by Heurico 1.16 in 58.8 seconds.