The generator matrix

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

generates a code of length 25 over GR(16,4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+81x^56+306x^60+372x^64+462x^68+768x^69+561x^72+4608x^73+660x^76+6912x^77+699x^80+486x^84+342x^88+102x^92+24x^96

The gray image is a code over GF(4) with n=100, k=7 and d=56.
This code was found by Heurico 1.16 in 0.806 seconds.