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 1 1 1 1 1 1 1 X 1 1 X 1 1 X 1 X X 1 1 1 1 1 1 1 1 1 1 1 0 X 0 0 0 0 X X X aX 0 X (a+1)X aX (a+1)X aX X X aX 0 (a+1)X aX X aX 0 X 0 (a+1)X aX X (a+1)X aX 0 0 aX aX X X aX aX X 0 0 aX (a+1)X 0 0 X aX 0 0 (a+1)X aX (a+1)X 0 aX (a+1)X X aX X X X X (a+1)X 0 (a+1)X aX X 0 X 0 aX aX aX aX X X (a+1)X 0 X (a+1)X X (a+1)X X 0 0 (a+1)X (a+1)X 0 (a+1)X X X 0 aX 0 0 0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX aX 0 aX (a+1)X aX (a+1)X (a+1)X 0 X (a+1)X 0 (a+1)X 0 aX aX aX aX (a+1)X 0 (a+1)X (a+1)X 0 0 (a+1)X X aX (a+1)X X X 0 X 0 aX aX 0 (a+1)X (a+1)X (a+1)X aX (a+1)X (a+1)X X X X X (a+1)X X X X (a+1)X (a+1)X aX aX (a+1)X 0 aX aX X 0 X 0 aX X aX 0 0 (a+1)X aX (a+1)X (a+1)X (a+1)X 0 0 0 X (a+1)X 0 0 0 aX aX (a+1)X 0 0 0 0 X 0 (a+1)X 0 X aX (a+1)X X X X 0 X (a+1)X X X (a+1)X (a+1)X (a+1)X aX 0 (a+1)X (a+1)X 0 X aX 0 (a+1)X 0 aX X X aX 0 aX X aX 0 X aX (a+1)X aX (a+1)X X aX aX (a+1)X aX aX aX aX (a+1)X aX 0 0 0 0 0 (a+1)X (a+1)X X X 0 X 0 0 X aX 0 0 (a+1)X (a+1)X aX aX (a+1)X X X X (a+1)X (a+1)X aX aX X 0 X X X 0 X (a+1)X (a+1)X 0 0 0 0 0 0 0 X X X (a+1)X X X X aX 0 0 0 aX X aX (a+1)X (a+1)X aX 0 aX X aX aX 0 0 (a+1)X (a+1)X (a+1)X aX X 0 0 X aX X (a+1)X X (a+1)X X X (a+1)X 0 aX 0 X 0 0 X aX X aX aX (a+1)X (a+1)X X 0 0 X (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X X (a+1)X (a+1)X X (a+1)X X (a+1)X 0 aX X aX (a+1)X aX 0 0 aX aX X (a+1)X X X (a+1)X X (a+1)X (a+1)X aX X aX 0 generates a code of length 96 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 272. Homogenous weight enumerator: w(x)=1x^0+78x^272+210x^276+48x^277+159x^280+288x^281+141x^284+768x^285+72x^288+1248x^289+96x^292+720x^293+51x^296+48x^300+27x^304+42x^308+36x^312+21x^316+12x^320+6x^324+6x^328+3x^332+6x^336+6x^340+3x^364 The gray image is a linear code over GF(4) with n=384, k=6 and d=272. This code was found by Heurico 1.16 in 0.43 seconds.