The generator matrix

 1  0  1  1  1  1  1  1  1  2  1  1  1  1 2a  1  1  1  1 2a+2  1  1  1  1  0  1  1  1  1  2  1  1  1  1 2a  1  1  1  1 2a+2  1  1  1  1  0  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1 2a 2a+2  2 2a 2a+2  0  1  1  1  1  1  1  2  2  1  1  1  2  1  1
 0  1 2a+3  a a+1  2 2a+1 a+2 a+3  1 2a  3 3a 3a+1  1 2a+2  1 3a+2 3a+3  1  0 2a+3  a a+1  1  2 2a+1 a+2 a+3  1 2a  3 3a 3a+1  1 2a+2  1 3a+2 3a+3  1  0 2a+3  a a+1  1  2 2a+1 a+2 a+3  1 2a  3 3a 3a+1 2a+2 2a+3 2a+1  a a+2 a+1 a+3  0  2 2a+3 2a+1  a a+1  0 a+2 a+3  2  1  1 3a 3a+1 3a 3a+1  1  1  1  1  1  2 3a+2 3a+3 2a  3 3a+2 3a+3 2a 2a+2 3a+2 3a+3 2a+2  0 2a 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+33x^292+12x^296+12x^300+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 41 seconds.