The generator matrix

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

generates a code of length 27 over GR(16,4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+120x^76+72x^77+144x^79+282x^80+72x^81+192x^84+24x^85+48x^87+36x^88+24x^89+9x^96

The gray image is a code over GF(4) with n=108, k=5 and d=76.
This code was found by Heurico 1.16 in 1.01e-007 seconds.