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 X 1 1 1 1 1 1 X 1 1 1 X X 1 1 X 1 X X 1 1 1 1 0 X 0 0 0 0 0 0 0 0 0 aX (a+1)X X (a+1)X X (a+1)X aX (a+1)X (a+1)X aX 0 (a+1)X aX X X (a+1)X aX aX X 0 aX aX aX 0 X aX (a+1)X 0 (a+1)X (a+1)X aX aX aX aX aX (a+1)X aX aX 0 0 0 0 aX X aX X 0 0 aX (a+1)X aX (a+1)X 0 (a+1)X X aX X X 0 0 X (a+1)X 0 X X X aX 0 0 0 X 0 0 0 0 X X X aX 0 aX (a+1)X (a+1)X (a+1)X aX (a+1)X (a+1)X X aX 0 X 0 aX X X X aX 0 aX aX aX (a+1)X X aX X aX (a+1)X aX X X (a+1)X (a+1)X aX aX 0 aX aX aX aX aX X 0 (a+1)X X X 0 X aX 0 0 aX X X 0 X aX aX (a+1)X 0 (a+1)X aX 0 (a+1)X aX X aX 0 0 0 0 X 0 0 X (a+1)X aX aX aX aX 0 (a+1)X aX aX (a+1)X aX (a+1)X 0 (a+1)X 0 aX (a+1)X 0 X aX aX 0 aX 0 (a+1)X (a+1)X aX X aX (a+1)X 0 aX (a+1)X 0 X (a+1)X aX X (a+1)X (a+1)X aX X aX X (a+1)X X 0 0 X X aX 0 X aX aX X X aX 0 (a+1)X (a+1)X (a+1)X 0 (a+1)X 0 0 X X 0 (a+1)X aX 0 0 0 0 0 X 0 (a+1)X 0 X aX (a+1)X aX (a+1)X 0 aX aX X 0 X aX aX X aX (a+1)X aX 0 0 0 0 (a+1)X aX (a+1)X 0 (a+1)X 0 X X (a+1)X (a+1)X aX 0 X (a+1)X (a+1)X 0 aX aX aX (a+1)X X (a+1)X aX aX 0 aX 0 (a+1)X X aX 0 X (a+1)X (a+1)X aX (a+1)X (a+1)X aX (a+1)X (a+1)X aX 0 X 0 X aX aX 0 0 X 0 0 0 0 0 X X X (a+1)X X X 0 (a+1)X X aX (a+1)X X X (a+1)X 0 (a+1)X X aX (a+1)X X 0 (a+1)X X X (a+1)X (a+1)X aX aX 0 0 X aX aX aX 0 0 0 (a+1)X X X X X 0 0 (a+1)X 0 0 X aX (a+1)X (a+1)X aX X 0 (a+1)X (a+1)X aX (a+1)X (a+1)X aX X 0 0 aX (a+1)X (a+1)X 0 0 0 aX 0 0 aX (a+1)X generates a code of length 79 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 212. Homogenous weight enumerator: w(x)=1x^0+66x^212+291x^216+399x^220+549x^224+1191x^228+2316x^232+4305x^236+4218x^240+1887x^244+270x^248+240x^252+198x^256+195x^260+141x^264+57x^268+39x^272+9x^276+6x^280+3x^284+3x^288 The gray image is a linear code over GF(4) with n=316, k=7 and d=212. This code was found by Heurico 1.16 in 3.8 seconds.