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 1 X 1 1 1 1 1 X 1 1 1 X X 1 1 1 1 1 1 1 1 1 1 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 aX 0 aX aX X X aX (a+1)X X X X X 0 aX 0 X aX 0 0 aX (a+1)X 0 0 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 X aX (a+1)X X aX X (a+1)X X 0 (a+1)X 0 aX X X X 0 aX 0 0 X aX X X (a+1)X 0 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 (a+1)X 0 (a+1)X aX X X (a+1)X (a+1)X X aX (a+1)X 0 0 0 (a+1)X aX (a+1)X (a+1)X X (a+1)X 0 X 0 aX X X aX 0 aX (a+1)X aX X aX aX (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 (a+1)X 0 aX (a+1)X 0 X aX aX 0 aX aX X X 0 aX aX 0 0 0 0 (a+1)X aX X X 0 aX aX X X 0 0 aX X (a+1)X 0 0 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 0 aX 0 aX X (a+1)X 0 aX 0 (a+1)X (a+1)X (a+1)X 0 0 aX aX aX aX X X X X aX (a+1)X (a+1)X (a+1)X (a+1)X aX 0 (a+1)X 0 0 (a+1)X 0 X 0 X generates a code of length 84 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 228. Homogenous weight enumerator: w(x)=1x^0+120x^228+318x^232+414x^236+12x^237+456x^240+180x^241+405x^244+1080x^245+330x^248+3240x^249+354x^252+4860x^253+330x^256+2916x^257+279x^260+288x^264+201x^268+210x^272+138x^276+84x^280+84x^284+39x^288+18x^292+24x^296+3x^316 The gray image is a linear code over GF(4) with n=336, k=7 and d=228. This code was found by Heurico 1.16 in 4.12 seconds.