The generator matrix

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

generates a code of length 29 over GR(16,4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+717x^80+966x^84+1269x^88+936x^92+180x^96+18x^100+3x^104+6x^112

The gray image is a code over GF(4) with n=116, k=6 and d=80.
This code was found by Heurico 1.16 in 0.281 seconds.