The generator matrix

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

generates a code of length 27 over GR(16,4) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+120x^78+45x^80+72x^86+18x^88

The gray image is a code over GF(4) with n=108, k=4 and d=78.
This code was found by Heurico 1.16 in 3.24e-008 seconds.