The generator matrix

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

generates a code of length 96 over GR(16,4) who´s minimum homogenous weight is 271.

Homogenous weight enumerator: w(x)=1x^0+660x^271+426x^272+660x^273+300x^274+2904x^275+1290x^276+1608x^277+660x^278+4236x^279+1626x^280+1932x^281+708x^282+5844x^283+1746x^284+2208x^285+648x^286+5940x^287+1746x^288+2280x^289+732x^290+5592x^291+1722x^292+2076x^293+612x^294+4872x^295+1512x^296+1692x^297+588x^298+2868x^299+1080x^300+936x^301+288x^302+1632x^303+525x^304+348x^305+72x^306+648x^307+63x^308+84x^309+132x^311+36x^312+3x^324

The gray image is a code over GF(4) with n=384, k=8 and d=271.
This code was found by Heurico 1.16 in 31.5 seconds.