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 1 1 1 1 1 1 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 a*X X a^2*X X X+a a^2*X X+1 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*X a*X a a^2*X+a^2 a*X a a*X+1 a^2*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 a^2*X+a^2 a^2*X X+a a*X+1 0 X+1 a^2 a^2*X+1 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+372x^218+864x^219+876x^220+816x^221+1560x^222+1644x^223+2151x^224+1932x^225+2124x^226+2376x^227+2766x^228+1740x^229+2496x^230+3384x^231+3126x^232+2172x^233+3468x^234+3684x^235+3264x^236+2220x^237+2868x^238+3072x^239+2883x^240+1824x^241+2424x^242+1860x^243+1926x^244+1152x^245+1164x^246+1116x^247+744x^248+360x^249+396x^250+384x^251+168x^252+72x^253+24x^254+48x^255+15x^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 38.3 seconds.