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

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

Homogenous weight enumerator: w(x)=1x^0+396x^218+756x^219+648x^220+1128x^221+1824x^222+1596x^223+1554x^224+1656x^225+2964x^226+2388x^227+2208x^228+2220x^229+3732x^230+2844x^231+2295x^232+2508x^233+3792x^234+2928x^235+2361x^236+2652x^237+3576x^238+2976x^239+2043x^240+1824x^241+3000x^242+2316x^243+1410x^244+1380x^245+1752x^246+804x^247+669x^248+348x^249+456x^250+252x^251+117x^252+108x^253+12x^254+36x^255+6x^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 46 seconds.