The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 a^2*X 1 1 0 1 0 1 X 1 1 1 a*X a^2*X 1 1 1 1 a^2*X 1 1 a*X 1 1 1 1 1 1 1 1 1 a*X 1 1 a^2*X 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 a*X 1 1 1 1 X 1 1 1 0 a*X 1 1 0 1 0 0 a^2*X 0 a^2*X 1 a^2*X+a a^2*X+1 X+1 X+1 a*X+a^2 a X+a^2 1 a*X+a X X X 1 a^2*X+1 1 1 a^2*X a^2*X+a 1 1 a^2 a^2*X+1 0 a*X+a 1 a a 1 X+a^2 a*X+1 a^2*X a*X a*X+a^2 a^2*X+1 a*X+a^2 X+a X+a^2 a^2*X a^2*X+a X+a^2 1 a X+1 a*X+1 1 a^2*X+a a*X 1 X+1 X+a X+a a^2*X+1 a^2*X+a a*X+a^2 X+a a^2*X a^2 1 X+a^2 a^2*X+a^2 X+a a*X+a^2 1 X+a^2 1 1 a*X 1 a^2*X+a^2 a 0 0 1 0 X a^2*X 0 a*X a*X a^2*X a^2*X a*X X 0 1 a X+a^2 a 1 a^2*X+1 a^2*X+1 X+1 a a^2*X+a a^2*X+a^2 X+1 X+a^2 a*X+1 X+a a*X+a^2 a a^2*X+a^2 X+a^2 a^2*X+a a^2*X+a^2 a^2*X a*X+a^2 a^2*X+1 X+1 a^2*X+1 X+1 a^2 a*X+1 a*X+a 0 1 X+a a*X+a a^2 a*X+a a a X+a^2 1 a^2 X a^2 0 a^2*X a^2*X+1 X+a^2 a*X+a^2 a*X+1 a^2*X+a^2 X+a X+1 a^2*X+a^2 X+a X+a a*X+1 a^2*X a*X+a a^2*X+1 1 1 0 0 X+1 0 0 0 1 a^2*X+1 a^2*X+a a^2 X+a^2 a^2*X+a^2 a*X+a a^2*X a*X+1 a a a*X+a^2 a*X+1 a*X+a a^2*X+a a^2*X+a^2 a*X+a^2 a^2*X+a^2 a^2*X+a a^2*X a^2*X+a a^2*X a*X X+a^2 a X+1 X+a^2 a^2 a^2*X+1 a*X a*X+1 0 a^2 a^2*X a^2 X a X+a 1 a^2*X+1 a^2*X+a a^2*X+a^2 a X a*X a^2*X+1 X+a^2 a^2*X+a^2 1 X X+a^2 X+a a a 1 0 a*X+1 a^2 a*X+a^2 a*X+1 a*X 0 1 a*X+a a*X+a X X 1 a*X+a^2 a*X+a 0 a*X+a^2 0 1 a*X generates a code of length 78 over F4[X]/(X^2) who´s minimum homogenous weight is 218. Homogenous weight enumerator: w(x)=1x^0+516x^218+708x^219+774x^220+444x^221+2148x^222+1740x^223+1605x^224+828x^225+3756x^226+2724x^227+1953x^228+984x^229+4968x^230+3264x^231+2274x^232+1152x^233+4956x^234+3420x^235+2427x^236+1068x^237+5040x^238+2928x^239+2058x^240+900x^241+3576x^242+2076x^243+1395x^244+456x^245+2028x^246+1248x^247+678x^248+288x^249+588x^250+288x^251+123x^252+24x^253+72x^254+36x^255+24x^256 The gray image is a linear code over GF(4) with n=312, k=8 and d=218. This code was found by Heurico 1.16 in 25.1 seconds.