The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 X 1 X 1 1 1 1 1 1 X X 0 X 0 0 0 0 X X X aX 0 X (a+1)X X (a+1)X (a+1)X (a+1)X aX X (a+1)X 0 (a+1)X aX X 0 aX X 0 0 (a+1)X (a+1)X (a+1)X (a+1)X 0 aX aX aX (a+1)X 0 aX aX 0 aX (a+1)X 0 aX X X 0 aX (a+1)X X X X 0 X X (a+1)X aX 0 X X aX X aX 0 aX X 0 aX 0 (a+1)X (a+1)X (a+1)X 0 X X X 0 0 0 X X aX X X 0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX X 0 0 (a+1)X 0 aX aX aX aX (a+1)X (a+1)X X X 0 (a+1)X X (a+1)X 0 (a+1)X aX aX X 0 0 0 (a+1)X 0 aX aX X aX X X X X aX (a+1)X (a+1)X (a+1)X (a+1)X aX aX X X aX 0 aX (a+1)X 0 0 (a+1)X (a+1)X aX (a+1)X aX X (a+1)X (a+1)X X aX X (a+1)X (a+1)X aX X X (a+1)X (a+1)X aX 0 X 0 0 0 0 0 X 0 (a+1)X 0 X aX (a+1)X X X X X 0 aX 0 aX 0 (a+1)X (a+1)X X X (a+1)X (a+1)X (a+1)X aX (a+1)X 0 aX aX aX (a+1)X aX X (a+1)X X (a+1)X X (a+1)X aX 0 (a+1)X 0 aX X X 0 aX aX X 0 aX aX aX X 0 (a+1)X 0 X X aX 0 aX 0 X 0 (a+1)X aX (a+1)X aX aX 0 0 (a+1)X 0 X aX X aX X (a+1)X (a+1)X aX 0 0 0 0 0 0 X X X (a+1)X X X X aX 0 aX X (a+1)X (a+1)X aX aX 0 aX (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X aX aX aX 0 0 X X aX (a+1)X X X aX 0 aX (a+1)X X X X aX 0 (a+1)X 0 (a+1)X 0 0 (a+1)X aX 0 0 X aX (a+1)X 0 (a+1)X X 0 X (a+1)X aX X X (a+1)X (a+1)X (a+1)X 0 (a+1)X 0 (a+1)X 0 X X 0 X (a+1)X X 0 aX (a+1)X (a+1)X X generates a code of length 86 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 244. Homogenous weight enumerator: w(x)=1x^0+147x^244+36x^247+213x^248+288x^251+135x^252+840x^255+144x^256+1152x^259+87x^260+756x^263+84x^264+36x^268+39x^272+33x^276+27x^280+9x^284+21x^288+18x^292+12x^296+12x^300+3x^304+3x^324 The gray image is a linear code over GF(4) with n=344, k=6 and d=244. This code was found by Heurico 1.16 in 0.521 seconds.