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 X 0 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 1 1 (a+1)X+a X+1 aX X (a+1)X X+1 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 aX+a+1 aX+a+1 X+a aX+a+1 (a+1)X+a+1 1 (a+1)X+a+1 a 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 aX+a+1 0 0 X+a+1 aX+a (a+1)X+a X+a+1 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+513x^224+612x^225+900x^226+1140x^227+1935x^228+1416x^229+1464x^230+2172x^231+2499x^232+2364x^233+2100x^234+2376x^235+3444x^236+2700x^237+2544x^238+2568x^239+3882x^240+2628x^241+2484x^242+2928x^243+3783x^244+2448x^245+1992x^246+2220x^247+2739x^248+2076x^249+1416x^250+1320x^251+1752x^252+804x^253+732x^254+528x^255+390x^256+288x^257+156x^258+108x^259+51x^260+24x^261+36x^262+3x^276 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 46.6 seconds.