The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 1 1 1 1 X 1 1 1 X 1 1 1 1 X 1 1 0 X 0 0 0 0 0 0 0 0 0 a*X a^2*X a*X X a*X a^2*X a*X X 0 a*X 0 a*X X X a^2*X a*X a*X 0 a^2*X X a^2*X a*X X a*X a*X a^2*X a*X a^2*X X a*X 0 0 a^2*X a*X 0 a^2*X a*X a*X X 0 0 a*X 0 X X a^2*X X 0 X X X X a*X 0 a*X a*X a^2*X X a^2*X a^2*X X X 0 0 a^2*X 0 0 a*X 0 0 0 X 0 0 0 0 X X X a*X 0 a*X a*X a*X a^2*X 0 a^2*X a^2*X X X a*X 0 X 0 a*X a*X X X a^2*X 0 a^2*X a^2*X a*X X 0 0 0 X X a*X 0 X X a*X a*X X a^2*X a^2*X a^2*X a*X 0 0 a^2*X a^2*X a^2*X a^2*X X 0 a*X X 0 a^2*X a^2*X a^2*X 0 X 0 a*X a*X a^2*X 0 a*X 0 a^2*X 0 X X 0 0 0 0 0 X 0 0 X a^2*X a*X a*X a*X 0 a^2*X a*X a*X X a^2*X a*X a*X 0 a^2*X X a^2*X X a*X X 0 X a*X 0 X X X 0 0 X a^2*X a^2*X a*X a*X X 0 0 a^2*X 0 X a^2*X 0 a^2*X a^2*X a*X X X a^2*X a^2*X X a*X a^2*X 0 0 0 0 X a^2*X 0 X a^2*X 0 a*X 0 X a^2*X 0 a^2*X a^2*X 0 a*X X a^2*X 0 0 0 0 0 X 0 a^2*X 0 X a*X a^2*X a^2*X X 0 0 a*X 0 a*X 0 X a*X X 0 a*X X a*X X a*X X 0 a*X a^2*X a^2*X a^2*X X a*X a*X X 0 a^2*X X a*X X a*X a^2*X a^2*X X 0 a^2*X a*X a^2*X 0 X a*X a*X 0 a*X a*X X 0 X a^2*X X a*X 0 a*X 0 0 0 a*X 0 X a*X a^2*X 0 a*X a*X a*X X a*X 0 0 0 0 0 X X X a^2*X X X a*X X 0 a*X a^2*X a^2*X a*X a*X a*X a*X a^2*X X a*X a*X a*X X a*X a*X a*X a^2*X 0 a^2*X 0 a^2*X 0 X 0 0 0 X X 0 a^2*X a*X X a*X a*X 0 0 a*X X a^2*X 0 a*X 0 a^2*X a^2*X a^2*X 0 0 a^2*X a*X a*X a^2*X X a*X X a^2*X a^2*X a^2*X 0 0 X a*X a*X a^2*X a*X a*X a*X generates a code of length 80 over F4[X]/(X^2) who´s minimum homogenous weight is 216. Homogenous weight enumerator: w(x)=1x^0+144x^216+306x^220+387x^224+12x^225+408x^228+180x^229+417x^232+1080x^233+363x^236+3240x^237+363x^240+4860x^241+285x^244+2916x^245+324x^248+300x^252+243x^256+183x^260+123x^264+129x^268+63x^272+36x^276+12x^280+3x^284+3x^288+3x^300 The gray image is a linear code over GF(4) with n=320, k=7 and d=216. This code was found by Heurico 1.16 in 3.76 seconds.