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 X 1 1 1 X 1 1 1 1 1 X 1 1 1 1 1 1 X X 1 1 1 X 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 X aX aX aX (a+1)X 0 aX aX (a+1)X (a+1)X aX 0 X 0 aX X 0 X aX aX X X 0 0 (a+1)X (a+1)X aX (a+1)X 0 aX X 0 X (a+1)X X X aX X 0 X (a+1)X 0 aX 0 0 X X (a+1)X (a+1)X (a+1)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 (a+1)X X 0 X aX (a+1)X aX 0 (a+1)X X 0 aX 0 X aX (a+1)X 0 X aX (a+1)X (a+1)X 0 aX aX aX aX (a+1)X 0 (a+1)X (a+1)X X (a+1)X X X (a+1)X X 0 X aX aX X aX aX X aX (a+1)X 0 aX aX 0 0 (a+1)X aX 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 0 X X X X X X 0 0 X (a+1)X 0 X aX aX aX (a+1)X aX aX aX aX X aX (a+1)X (a+1)X X aX (a+1)X X X X (a+1)X X aX X X (a+1)X aX aX (a+1)X X X aX 0 X X X (a+1)X 0 0 (a+1)X aX 0 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 0 aX aX (a+1)X (a+1)X (a+1)X aX aX aX aX (a+1)X X aX X 0 aX X aX X X aX (a+1)X (a+1)X aX 0 aX 0 X 0 (a+1)X (a+1)X X X aX X X X aX 0 X 0 aX (a+1)X X (a+1)X X X (a+1)X aX (a+1)X X aX 0 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 aX (a+1)X (a+1)X aX (a+1)X aX X aX 0 (a+1)X 0 0 aX X 0 0 X 0 aX X aX aX (a+1)X (a+1)X (a+1)X (a+1)X X 0 0 aX aX aX (a+1)X aX 0 X aX (a+1)X aX X 0 aX 0 X (a+1)X aX 0 aX 0 (a+1)X 0 (a+1)X generates a code of length 78 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 212. Homogenous weight enumerator: w(x)=1x^0+210x^212+390x^216+537x^220+822x^224+1962x^228+4050x^232+4680x^236+2499x^240+279x^244+282x^248+219x^252+162x^256+123x^260+87x^264+45x^268+18x^272+6x^276+3x^280+3x^284+6x^288 The gray image is a linear code over GF(4) with n=312, k=7 and d=212. This code was found by Heurico 1.16 in 55.2 seconds.