The generator matrix

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

generates a code of length 78 over GR(16,4) who´s minimum homogenous weight is 222.

Homogenous weight enumerator: w(x)=1x^0+516x^222+492x^223+306x^224+252x^225+1428x^226+876x^227+477x^228+396x^229+1548x^230+1008x^231+666x^232+264x^233+1332x^234+696x^235+390x^236+264x^237+1044x^238+636x^239+357x^240+144x^241+828x^242+468x^243+195x^244+144x^245+708x^246+240x^247+120x^248+60x^249+252x^250+168x^251+36x^252+12x^253+24x^254+24x^255+6x^256+6x^260

The gray image is a code over GF(4) with n=312, k=7 and d=222.
This code was found by Heurico 1.16 in 1.59 seconds.