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

generates a code of length 97 over GR(16,4) who´s minimum homogenous weight is 279.

Homogenous weight enumerator: w(x)=1x^0+1020x^279+513x^280+2292x^283+864x^284+2592x^287+699x^288+2064x^291+648x^292+1392x^295+507x^296+1080x^299+411x^300+1044x^303+174x^304+516x^307+234x^308+240x^311+42x^312+48x^315+3x^316

The gray image is a code over GF(4) with n=388, k=7 and d=279.
This code was found by Heurico 1.16 in 5.28 seconds.