The generator matrix

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

generates a code of length 78 over GR(16,4) who´s minimum homogenous weight is 227.

Homogenous weight enumerator: w(x)=1x^0+816x^227+264x^228+1152x^231+396x^232+336x^235+144x^236+12x^240+336x^243+168x^244+384x^247+36x^248+48x^251+3x^256

The gray image is a code over GF(4) with n=312, k=6 and d=227.
This code was found by Heurico 1.16 in 79.7 seconds.