The generator matrix

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

generates a code of length 96 over GR(16,4) who´s minimum homogenous weight is 276.

Homogenous weight enumerator: w(x)=1x^0+1422x^276+3012x^280+3117x^284+2997x^288+1989x^292+1632x^296+1056x^300+810x^304+282x^308+60x^312+3x^316+3x^324

The gray image is a code over GF(4) with n=384, k=7 and d=276.
This code was found by Heurico 1.16 in 87.3 seconds.