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 aX (a+1)X aX X aX (a+1)X aX X 0 aX 0 aX X X (a+1)X aX aX 0 (a+1)X X (a+1)X aX X aX aX (a+1)X aX (a+1)X X aX 0 0 (a+1)X aX 0 (a+1)X aX aX X 0 0 aX 0 X X (a+1)X X 0 X X X X aX 0 aX aX (a+1)X X (a+1)X (a+1)X X X 0 0 (a+1)X 0 0 aX 0 0 0 X 0 0 0 0 X X X aX 0 aX aX aX (a+1)X 0 (a+1)X (a+1)X X X aX 0 X 0 aX aX X X (a+1)X 0 (a+1)X (a+1)X aX X 0 0 0 X X aX 0 X X aX aX X (a+1)X (a+1)X (a+1)X aX 0 0 (a+1)X (a+1)X (a+1)X (a+1)X X 0 aX X 0 (a+1)X (a+1)X (a+1)X 0 X 0 aX aX (a+1)X 0 aX 0 (a+1)X 0 X X 0 0 0 0 0 X 0 0 X (a+1)X aX aX aX 0 (a+1)X aX aX X (a+1)X aX aX 0 (a+1)X X (a+1)X X aX X 0 X aX 0 X X X 0 0 X (a+1)X (a+1)X aX aX X 0 0 (a+1)X 0 X (a+1)X 0 (a+1)X (a+1)X aX X X (a+1)X (a+1)X X aX (a+1)X 0 0 0 0 X (a+1)X 0 X (a+1)X 0 aX 0 X (a+1)X 0 (a+1)X (a+1)X 0 aX X (a+1)X 0 0 0 0 0 X 0 (a+1)X 0 X aX (a+1)X (a+1)X X 0 0 aX 0 aX 0 X aX X 0 aX X aX X aX X 0 aX (a+1)X (a+1)X (a+1)X X aX aX X 0 (a+1)X X aX X aX (a+1)X (a+1)X X 0 (a+1)X aX (a+1)X 0 X aX aX 0 aX aX X 0 X (a+1)X X aX 0 aX 0 0 0 aX 0 X aX (a+1)X 0 aX aX aX X aX 0 0 0 0 0 X X X (a+1)X X X aX X 0 aX (a+1)X (a+1)X aX aX aX aX (a+1)X X aX aX aX X aX aX aX (a+1)X 0 (a+1)X 0 (a+1)X 0 X 0 0 0 X X 0 (a+1)X aX X aX aX 0 0 aX X (a+1)X 0 aX 0 (a+1)X (a+1)X (a+1)X 0 0 (a+1)X aX aX (a+1)X X aX X (a+1)X (a+1)X (a+1)X 0 0 X aX aX (a+1)X aX aX aX generates a code of length 80 over F4[X,sigma]/(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 3.88 seconds.