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 X 1 1 (a+1)X 1 1 0 1 1 1 1 1 1 (a+1)X 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 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 0 X+a aX+a+1 (a+1)X 1 1 (a+1)X+1 X+a 1 X 1 aX X+1 1 (a+1)X+a X+a+1 1 (a+1)X+a (a+1)X+a+1 aX+1 1 X a+1 1 aX+a aX+a+1 aX+a+1 aX X+a (a+1)X+1 aX X+a 1 (a+1)X+1 aX X+a aX a+1 (a+1)X+a (a+1)X 1 X+a X+1 aX aX+1 X+a 0 1 (a+1)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 X aX 0 aX aX X (a+1)X (a+1)X X aX (a+1)X (a+1)X (a+1)X 0 X (a+1)X X (a+1)X 0 aX 0 (a+1)X aX 0 0 0 (a+1)X (a+1)X aX 0 X aX (a+1)X aX aX 0 X (a+1)X 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 aX 0 (a+1)X X X 0 (a+1)X (a+1)X (a+1)X aX (a+1)X 0 X X X X (a+1)X aX (a+1)X (a+1)X 0 0 X 0 (a+1)X aX 0 aX (a+1)X 0 (a+1)X X X aX aX 0 0 aX 0 0 (a+1)X 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 0 X aX 0 0 (a+1)X 0 (a+1)X X X 0 aX aX (a+1)X X 0 (a+1)X 0 X 0 aX aX 0 X (a+1)X X (a+1)X aX aX aX X X (a+1)X (a+1)X X aX X (a+1)X 0 generates a code of length 77 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 216. Homogenous weight enumerator: w(x)=1x^0+276x^216+228x^217+132x^218+795x^220+624x^221+408x^222+1017x^224+1056x^225+564x^226+1263x^228+1056x^229+516x^230+1179x^232+1344x^233+684x^234+1233x^236+1008x^237+480x^238+915x^240+624x^241+252x^242+291x^244+192x^245+36x^246+87x^248+12x^249+30x^252+21x^256+24x^260+18x^264+6x^268+6x^272+6x^276 The gray image is a linear code over GF(4) with n=308, k=7 and d=216. This code was found by Heurico 1.16 in 2 seconds.