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

generates a code of length 97 over GR(16,4) who´s minimum homogenous weight is 291.

Homogenous weight enumerator: w(x)=1x^0+192x^291+21x^292+36x^296+3x^304+3x^308

The gray image is a code over GF(4) with n=388, k=4 and d=291.
This code was found by Heurico 1.16 in 0.375 seconds.