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 X 1 1 X X 1 1 1 1 1 (a+1)X 1 1 1 1 X 1 (a+1)X 1 1 1 1 1 (a+1)X 1 1 1 X 1 1 aX 1 1 1 (a+1)X 1 1 (a+1)X 1 1 (a+1)X (a+1)X 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 aX+a+1 a+1 aX+1 aX X+a a+1 0 1 1 (a+1)X+a+1 1 aX+a aX+a 1 1 (a+1)X+a+1 (a+1)X+a aX (a+1)X+a X+1 1 (a+1)X+a+1 aX+1 (a+1)X X 1 (a+1)X 1 (a+1)X+a+1 X+1 aX (a+1)X+a (a+1)X+1 1 aX aX+a+1 (a+1)X+a 1 aX+a+1 a+1 1 a (a+1)X X+a 1 X+a+1 X+1 1 1 (a+1)X 1 1 (a+1)X+a 0 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 aX X X aX (a+1)X X X aX (a+1)X aX (a+1)X (a+1)X (a+1)X aX X aX aX X 0 aX X aX aX (a+1)X X (a+1)X aX (a+1)X aX aX 0 aX X (a+1)X aX 0 X X (a+1)X (a+1)X X (a+1)X aX X (a+1)X aX 0 (a+1)X (a+1)X 0 X 0 0 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 (a+1)X (a+1)X X 0 (a+1)X (a+1)X aX (a+1)X X X (a+1)X (a+1)X (a+1)X X 0 0 X aX aX aX 0 aX (a+1)X X 0 X 0 X (a+1)X X aX X 0 0 (a+1)X 0 X aX 0 aX (a+1)X aX (a+1)X X 0 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 X aX X 0 aX (a+1)X 0 (a+1)X aX X aX 0 (a+1)X 0 0 (a+1)X 0 X 0 X aX (a+1)X X aX 0 X (a+1)X aX X aX aX 0 aX aX X (a+1)X (a+1)X (a+1)X X (a+1)X 0 0 (a+1)X X X generates a code of length 79 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 220. Homogenous weight enumerator: w(x)=1x^0+84x^220+72x^221+24x^222+453x^224+456x^225+276x^226+1074x^228+780x^229+444x^230+1104x^232+1032x^233+492x^234+1176x^236+1428x^237+720x^238+1374x^240+984x^241+780x^242+1017x^244+948x^245+252x^246+591x^248+408x^249+84x^250+141x^252+36x^253+54x^256+33x^260+18x^264+9x^268+18x^272+12x^276+3x^280+6x^284 The gray image is a linear code over GF(4) with n=316, k=7 and d=220. This code was found by Heurico 1.16 in 1.83 seconds.