The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 X 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 (a+1)X 1 1 X 1 1 1 1 X 1 aX 1 (a+1)X 1 1 aX 1 1 1 1 1 1 1 1 1 1 1 0 aX 1 1 1 (a+1)X 1 1 1 1 1 1 1 1 1 (a+1)X 1 1 1 1 0 1 1 a a+1 0 (a+1)X+1 (a+1)X+a+1 a 1 0 (a+1)X+1 (a+1)X+a+1 1 a X (a+1)X+a+1 1 (a+1)X+1 a aX+a+1 0 aX+1 1 a (a+1)X+a+1 aX+1 (a+1)X+a+1 aX X+a aX+a+1 0 1 1 (a+1)X+1 X+a 1 aX X+a aX+a+1 (a+1)X+a 1 X+1 1 aX+a+1 1 (a+1)X aX+a 1 aX+1 X+a+1 (a+1)X+a+1 (a+1)X+1 X+1 (a+1)X (a+1)X aX+a+1 X+a+1 aX+a+1 aX+1 1 1 1 1 (a+1)X+a+1 1 X 0 (a+1)X X+1 1 X+a (a+1)X X+1 X+1 1 0 aX+a (a+1)X+a X 0 0 (a+1)X 0 0 0 X aX X X X (a+1)X (a+1)X aX aX aX 0 0 X aX (a+1)X aX (a+1)X (a+1)X (a+1)X aX X aX X aX (a+1)X X X aX aX (a+1)X aX aX (a+1)X (a+1)X X aX 0 aX X X aX aX (a+1)X aX aX (a+1)X (a+1)X aX (a+1)X (a+1)X X X 0 (a+1)X (a+1)X (a+1)X 0 aX (a+1)X X (a+1)X aX (a+1)X X (a+1)X aX X 0 X 0 (a+1)X X (a+1)X X 0 0 0 X 0 X (a+1)X (a+1)X X (a+1)X 0 (a+1)X X X 0 X (a+1)X 0 (a+1)X 0 0 X (a+1)X (a+1)X X aX (a+1)X (a+1)X X (a+1)X (a+1)X 0 0 X aX 0 (a+1)X X X (a+1)X X (a+1)X (a+1)X (a+1)X aX X 0 (a+1)X (a+1)X X (a+1)X aX X X 0 aX (a+1)X X aX aX 0 0 (a+1)X aX aX 0 X aX 0 0 aX aX X aX 0 X (a+1)X 0 (a+1)X (a+1)X 0 0 0 0 (a+1)X (a+1)X (a+1)X (a+1)X 0 aX X aX 0 aX (a+1)X X X (a+1)X X aX X (a+1)X 0 (a+1)X aX X 0 0 X aX (a+1)X (a+1)X aX (a+1)X (a+1)X 0 aX aX X X X (a+1)X aX 0 0 0 0 (a+1)X aX aX X X aX X aX X (a+1)X aX (a+1)X 0 X (a+1)X 0 0 aX (a+1)X 0 X (a+1)X 0 X 0 0 0 X aX 0 aX X 0 generates a code of length 80 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 224. Homogenous weight enumerator: w(x)=1x^0+81x^224+132x^225+396x^227+447x^228+516x^229+828x^231+612x^232+864x^233+876x^235+582x^236+1212x^237+1248x^239+750x^240+1092x^241+1188x^243+678x^244+1404x^245+924x^247+561x^248+696x^249+516x^251+192x^252+228x^253+168x^255+75x^256+33x^260+15x^264+21x^268+18x^272+12x^276+6x^280+3x^284+9x^288 The gray image is a linear code over GF(4) with n=320, k=7 and d=224. This code was found by Heurico 1.16 in 1.86 seconds.