The generator matrix

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

generates a code of length 78 over GR(16,4) who´s minimum homogenous weight is 223.

Homogenous weight enumerator: w(x)=1x^0+1308x^223+594x^224+2292x^227+918x^228+2556x^231+645x^232+2148x^235+708x^236+1500x^239+480x^240+1332x^243+510x^244+828x^247+213x^248+276x^251+15x^252+48x^255+3x^256+6x^260+3x^268

The gray image is a code over GF(4) with n=312, k=7 and d=223.
This code was found by Heurico 1.16 in 891 seconds.