The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 X 1 1 a*X 1 1 1 0 1 1 1 1 1 a^2*X 1 1 1 1 1 1 1 1 1 0 1 a*X 1 1 1 1 a^2*X a^2*X 1 1 1 a*X 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 X 1 a*X 1 1 0 1 1 a a^2 0 a^2*X+1 a^2*X+a^2 a 1 0 a^2*X+1 a 1 a^2*X+a^2 X a^2*X+a^2 X+a a^2*X+1 1 a^2*X+a^2 a 1 0 a^2*X+a a^2 1 X+1 a*X a^2*X+1 X a*X+a^2 1 a^2*X+a X+a^2 X a*X+a a^2 X+1 X+a a^2 X+a^2 1 a^2*X+a 1 a*X a^2*X+a^2 a^2*X+1 X+a 1 1 a*X+a^2 a*X+a X 1 X X+1 a*X a*X 0 a*X+a a*X+1 a*X+a^2 X+a^2 a^2*X+a^2 a^2*X+a^2 a^2*X+a^2 a^2*X 1 1 1 a^2*X+1 1 1 1 1 1 0 0 a^2*X 0 0 0 X X X X X X a^2*X a^2*X a*X X a*X a^2*X a^2*X 0 a^2*X a^2*X a*X a^2*X 0 0 a*X X 0 a*X 0 a^2*X X 0 0 X a^2*X 0 a^2*X X a^2*X 0 a*X 0 X X a^2*X X 0 a*X X X 0 X X a*X X a^2*X X a*X X a^2*X a^2*X 0 a^2*X X X 0 0 a*X 0 a*X X 0 a*X a^2*X X 0 0 0 X 0 X a^2*X 0 X a^2*X X 0 a*X a^2*X 0 a^2*X 0 0 a*X a*X X X a^2*X a^2*X a^2*X a*X a*X 0 a*X X X a^2*X 0 0 0 a^2*X a^2*X a^2*X 0 X X a^2*X X a^2*X a^2*X X 0 0 a^2*X a*X X a^2*X a*X X 0 X a*X a*X 0 0 X X 0 a^2*X X X X X a*X X a^2*X 0 X X a*X a^2*X a*X 0 0 0 0 a^2*X a^2*X X a^2*X a*X 0 a^2*X X X a*X X a*X a*X X a^2*X a^2*X 0 a^2*X a^2*X X 0 a^2*X a^2*X a^2*X 0 0 a*X 0 a*X a^2*X a*X a^2*X a^2*X a*X a*X 0 X X X a^2*X a^2*X a*X a^2*X a*X a*X X a*X X X X 0 X a*X 0 0 X a^2*X 0 X a^2*X a*X a^2*X X X X 0 a^2*X a^2*X X a^2*X 0 0 X generates a code of length 77 over F4[X]/(X^2) who´s minimum homogenous weight is 216. Homogenous weight enumerator: w(x)=1x^0+183x^216+228x^217+156x^218+774x^220+696x^221+348x^222+1140x^224+888x^225+576x^226+1104x^228+1164x^229+660x^230+1422x^232+1296x^233+444x^234+1287x^236+1104x^237+612x^238+864x^240+552x^241+264x^242+222x^244+204x^245+12x^246+54x^248+12x^249+36x^252+30x^256+12x^260+9x^264+15x^268+9x^272+6x^276 The gray image is a linear code over GF(4) with n=308, k=7 and d=216. This code was found by Heurico 1.16 in 1.79 seconds.