The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a^2*X a^2*X 1 1 1 1 0 1 1 1 1 a^2*X 1 1 a*X 1 1 1 1 1 1 a*X 1 1 a*X a*X 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 a^2*X 1 1 1 1 1 1 1 a^2*X X a^2*X 1 1 1 0 1 0 0 0 a^2*X 1 a^2*X+a a^2 a^2*X+1 a^2*X+1 a a^2*X+a^2 a^2 1 1 a^2*X+a 1 a^2*X+a^2 a 1 a*X+a^2 a^2*X+1 X+a a*X 1 X+1 X+1 1 X+a^2 a*X a a^2*X+a^2 a^2*X+1 X+a 1 X a*X+a X 1 a^2 X a^2*X a*X+1 a^2*X+a^2 0 a*X+a a*X+1 X+a^2 a a X+1 X 1 1 X+a^2 X X 1 X+a a*X+a a^2 X+1 a 0 a*X+1 X+1 a^2*X+a^2 X a^2*X+1 a^2*X+1 a^2*X+1 1 1 1 1 a^2*X+a X 0 0 1 1 a a^2 1 X+1 1 a 0 X a*X+a a^2 X+1 a^2 X+a^2 a^2 0 a*X+a X+a X+1 a 0 X+1 a X+1 a^2*X X+1 a^2*X a*X+a a^2*X+a 1 a*X+a^2 X+1 X 0 a*X+a^2 1 a^2*X+a^2 a*X+a X 1 a a^2*X+a^2 a*X+a^2 a^2 1 a^2*X X+a X a*X+a^2 a*X+1 a^2*X a^2*X+a^2 X a a^2*X+a^2 a X+a a*X+1 a*X+a^2 a^2*X+a 0 1 a*X+a^2 a*X+1 a*X+1 X+a^2 X+a^2 X+a^2 X+a^2 0 1 a^2*X+a X+a a*X+a^2 X 0 0 0 a^2*X 0 0 0 X X X a^2*X a*X a*X a*X a*X a^2*X a^2*X X a^2*X X a*X 0 a^2*X a*X X X a*X a*X a^2*X X a*X a*X a^2*X 0 a^2*X a^2*X X a^2*X 0 0 0 X X a*X X a*X 0 0 0 X X 0 a^2*X X a*X a^2*X X 0 X 0 a^2*X X a^2*X a*X X a^2*X a^2*X X a^2*X a^2*X X X X 0 a^2*X X a*X X 0 0 0 0 X a^2*X a*X X a^2*X a*X a*X X 0 a*X X a*X X a^2*X X a*X 0 X 0 a*X 0 0 0 a^2*X a*X X a^2*X a*X a^2*X 0 X a^2*X a^2*X a*X a^2*X a*X a*X X X 0 a*X a*X 0 a^2*X X a^2*X 0 a*X a*X 0 a*X 0 X X a^2*X 0 0 0 a*X 0 a^2*X a^2*X X X X a*X X 0 a*X a*X X 0 a^2*X a^2*X generates a code of length 78 over F4[X]/(X^2) who´s minimum homogenous weight is 216. Homogenous weight enumerator: w(x)=1x^0+378x^216+84x^217+492x^219+2115x^220+804x^221+1200x^223+4077x^224+1344x^225+1668x^227+6138x^228+2112x^229+2040x^231+7770x^232+2520x^233+2340x^235+7698x^236+2112x^237+2208x^239+6324x^240+1872x^241+1500x^243+4164x^244+1056x^245+696x^247+1920x^248+324x^249+144x^251+240x^252+60x^253+69x^256+21x^260+18x^264+18x^268+3x^272+3x^276+3x^284 The gray image is a linear code over GF(4) with n=312, k=8 and d=216. This code was found by Heurico 1.16 in 23.5 seconds.