The generator matrix

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

generates a code of length 97 over GR(16,4) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+153x^272+396x^273+708x^275+1116x^276+2148x^277+1632x^279+1608x^280+3264x^281+2196x^283+2109x^284+4200x^285+3096x^287+2598x^288+5388x^289+3156x^291+2760x^292+5136x^293+3012x^295+2433x^296+4656x^297+2508x^299+1854x^300+3252x^301+1440x^303+894x^304+1584x^305+552x^307+552x^308+612x^309+132x^311+207x^312+72x^313+30x^316+12x^317+15x^320+21x^324+21x^328+3x^332+3x^336+3x^340+3x^344

The gray image is a code over GF(4) with n=388, k=8 and d=272.
This code was found by Heurico 1.16 in 30.5 seconds.