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 X 1 X 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 (a+1)X aX 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 0 X (a+1)X aX aX (a+1)X 0 X aX 0 X 0 X 0 X X 0 aX 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 aX X 0 (a+1)X (a+1)X (a+1)X 0 (a+1)X 0 aX X X X X 0 (a+1)X X aX aX 0 (a+1)X X 0 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 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 0 (a+1)X X X 0 0 X X X X aX aX aX aX (a+1)X 0 X 0 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 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 0 X 0 aX aX (a+1)X 0 0 0 0 X aX (a+1)X X X (a+1)X 0 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 0 (a+1)X 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 (a+1)X 0 (a+1)X X aX aX 0 (a+1)X aX aX 0 (a+1)X aX aX (a+1)X aX aX aX 0 generates a code of length 83 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 224. Homogenous weight enumerator: w(x)=1x^0+66x^224+285x^228+411x^232+60x^235+396x^236+420x^239+399x^240+1560x^243+414x^244+3720x^247+384x^248+4332x^251+297x^252+2196x^255+273x^256+267x^260+294x^264+189x^268+141x^272+96x^276+72x^280+54x^284+36x^288+15x^292+3x^296+3x^308 The gray image is a linear code over GF(4) with n=332, k=7 and d=224. This code was found by Heurico 1.16 in 4.04 seconds.