The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 (a+1)X 1 1 1 1 aX 1 1 1 1 1 1 1 0 aX 1 1 1 (a+1)X 1 aX 1 1 1 1 (a+1)X 1 0 0 1 1 1 X 1 1 1 1 1 1 1 aX 1 1 1 (a+1)X 1 aX 1 1 1 1 1 1 X 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 (a+1)X 0 (a+1)X 1 (a+1)X+a a+1 X 0 X X X+a X+1 X+a+1 1 a a+1 (a+1)X (a+1)X+a+1 X+1 0 aX+a 1 1 (a+1)X+1 a X+a+1 1 aX+a+1 1 aX+a (a+1)X+a a aX+a+1 aX (a+1)X+a+1 1 1 (a+1)X (a+1)X+1 a 1 1 (a+1)X+a+1 (a+1)X+a aX+a+1 (a+1)X+a+1 X+1 (a+1)X 1 1 aX+a X+a 1 a+1 1 aX+a+1 0 a (a+1)X+1 aX+a (a+1)X+1 1 (a+1)X+1 1 0 a+1 (a+1)X+a a+1 aX+a aX+1 aX aX+1 X+a+1 (a+1)X+a (a+1)X+a aX+a 0 0 1 0 X aX 0 (a+1)X (a+1)X (a+1)X (a+1)X+1 (a+1)X+1 1 a X+1 a+1 a aX+a+1 (a+1)X+a 1 aX+a+1 X+1 X+a a+1 X+1 (a+1)X aX aX+1 (a+1)X+a+1 X+a X+a X a (a+1)X aX+a aX+a+1 a 1 (a+1)X (a+1)X+a X+a aX+1 X+a+1 a (a+1)X aX+1 (a+1)X+a+1 X+a+1 (a+1)X+a+1 aX+a+1 X (a+1)X+a aX+1 aX+a+1 (a+1)X+1 a (a+1)X+1 (a+1)X+a (a+1)X+a+1 X+a X aX+a X+1 (a+1)X+a+1 (a+1)X a+1 1 1 a+1 aX (a+1)X+a aX+1 a+1 a aX+a a+1 aX (a+1)X+a (a+1)X 0 0 0 0 1 (a+1)X+1 a a+1 (a+1)X+a+1 X+a+1 aX+a+1 a+1 X+a (a+1)X+1 1 X (a+1)X+a+1 X+a+1 a X+a+1 a+1 aX+1 (a+1)X+1 (a+1)X+1 aX X+1 a X+a+1 X+1 a X+a a+1 (a+1)X+a (a+1)X+a 1 0 a+1 0 aX+a+1 (a+1)X X+1 aX aX 1 X+1 1 X (a+1)X+a aX X+a+1 aX X+a (a+1)X+a+1 X+1 aX+a (a+1)X+a+1 a (a+1)X+a X (a+1)X a 1 aX+1 (a+1)X+a 1 aX aX+1 X+a+1 (a+1)X+1 aX+1 (a+1)X+1 (a+1)X+a (a+1)X+a+1 a (a+1)X 0 0 aX+a+1 aX+a+1 0 aX 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+528x^224+660x^225+792x^226+696x^227+1740x^228+2616x^229+1632x^230+876x^231+2490x^232+3312x^233+2748x^234+1236x^235+3225x^236+3720x^237+2508x^238+1452x^239+3408x^240+4272x^241+2952x^242+1320x^243+3318x^244+3948x^245+2232x^246+1032x^247+2694x^248+2772x^249+1548x^250+696x^251+1455x^252+1380x^253+732x^254+336x^255+471x^256+360x^257+216x^258+36x^259+120x^260+6x^268 The gray image is a linear code over GF(4) with n=320, k=8 and d=224. This code was found by Heurico 1.16 in 60 seconds.