The generator matrix

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

generates a code of length 28 over GR(16,4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+81x^80+576x^82+96x^84+72x^88+192x^90+3x^96+3x^112

The gray image is a code over GF(4) with n=112, k=5 and d=80.
This code was found by Heurico 1.16 in -1.01e-007 seconds.