The generator matrix

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

generates a code of length 27 over GR(16,4) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+198x^64+351x^68+48x^69+441x^72+576x^73+558x^76+2592x^77+546x^80+5184x^81+696x^84+3888x^85+630x^88+426x^92+159x^96+81x^100+9x^104

The gray image is a code over GF(4) with n=108, k=7 and d=64.
This code was found by Heurico 1.16 in 0.995 seconds.