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 X X 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 0 X 0 0 0 0 0 0 0 0 0 aX (a+1)X aX X aX (a+1)X aX X 0 aX 0 aX X X (a+1)X aX aX 0 (a+1)X X aX (a+1)X X aX aX (a+1)X aX (a+1)X X aX 0 0 (a+1)X aX 0 (a+1)X aX aX X 0 0 aX 0 X X (a+1)X X 0 X X X X aX aX aX (a+1)X 0 aX 0 (a+1)X (a+1)X (a+1)X X 0 X X 0 0 X 0 0 0 0 X X X aX 0 aX aX aX (a+1)X 0 (a+1)X (a+1)X X X aX 0 X 0 aX aX X X (a+1)X 0 (a+1)X (a+1)X aX X 0 0 0 X X aX 0 X X aX aX X (a+1)X (a+1)X (a+1)X aX 0 0 (a+1)X (a+1)X (a+1)X (a+1)X X 0 aX X 0 (a+1)X (a+1)X 0 X (a+1)X X 0 0 X (a+1)X X aX X aX (a+1)X 0 0 0 X 0 0 X (a+1)X aX aX aX 0 (a+1)X aX aX X (a+1)X aX aX 0 (a+1)X X (a+1)X X aX X 0 X aX 0 X X X 0 0 X (a+1)X (a+1)X aX aX X 0 0 (a+1)X 0 X (a+1)X 0 (a+1)X (a+1)X aX X X (a+1)X (a+1)X X aX (a+1)X 0 0 0 0 X (a+1)X X (a+1)X X aX aX (a+1)X X aX aX 0 (a+1)X 0 X 0 0 0 0 X 0 (a+1)X 0 X aX (a+1)X (a+1)X X 0 0 aX 0 aX 0 X aX X 0 aX X aX X aX X 0 aX (a+1)X (a+1)X (a+1)X X aX aX X 0 (a+1)X X aX X aX (a+1)X (a+1)X X 0 (a+1)X aX (a+1)X 0 X aX aX 0 aX aX X 0 X (a+1)X X aX aX 0 0 aX 0 X aX aX X 0 (a+1)X (a+1)X aX 0 0 0 0 0 X X X (a+1)X X X aX X 0 aX (a+1)X (a+1)X aX aX aX aX (a+1)X X aX aX aX X aX aX aX (a+1)X (a+1)X 0 0 (a+1)X 0 X 0 0 0 X X 0 (a+1)X aX X aX aX 0 0 aX X (a+1)X 0 aX 0 (a+1)X (a+1)X (a+1)X 0 0 (a+1)X aX aX X aX (a+1)X (a+1)X (a+1)X X aX X X aX aX X aX generates a code of length 77 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 208. Homogenous weight enumerator: w(x)=1x^0+156x^208+345x^212+411x^216+48x^219+387x^220+576x^223+468x^224+2592x^227+420x^228+5184x^231+282x^232+3888x^235+306x^236+324x^240+297x^244+210x^248+159x^252+156x^256+51x^260+57x^264+48x^268+15x^272+3x^292 The gray image is a linear code over GF(4) with n=308, k=7 and d=208. This code was found by Heurico 1.16 in 3.71 seconds.