The generator matrix

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

generates a code of length 78 over GR(16,4) who´s minimum homogenous weight is 218.

Homogenous weight enumerator: w(x)=1x^0+480x^218+720x^219+753x^220+588x^221+2376x^222+1596x^223+1518x^224+1044x^225+3708x^226+2352x^227+2547x^228+1224x^229+4020x^230+2772x^231+2595x^232+1368x^233+4632x^234+3396x^235+2862x^236+1212x^237+4572x^238+2772x^239+2238x^240+1260x^241+3684x^242+2064x^243+1515x^244+696x^245+2052x^246+900x^247+663x^248+264x^249+552x^250+300x^251+147x^252+24x^253+36x^254+24x^255+9x^256

The gray image is a code over GF(4) with n=312, k=8 and d=218.
This code was found by Heurico 1.16 in 26.2 seconds.