The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+189x^80+768x^84+63x^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 0.344 seconds.