The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (a+1)X 1 1 X 1 1 1 1 1 1 0 1 1 1 1 1 1 (a+1)X 1 (a+1)X 1 1 1 1 1 X 1 1 0 1 1 1 aX 1 1 aX 1 1 X 0 1 1 aX 0 1 1 aX 1 1 1 1 1 1 X 1 1 X 1 1 1 aX 1 1 1 1 1 1 1 1 1 0 1 0 0 (a+1)X X (a+1)X aX aX aX 1 (a+1)X+a a+1 X+1 a+1 (a+1)X+1 X+1 a (a+1)X+1 1 (a+1)X+a X+a 1 (a+1)X+a+1 X+1 1 (a+1)X+1 1 aX+a 1 aX 1 (a+1)X+a+1 (a+1)X+a+1 X a 1 X+a 1 aX+a+1 (a+1)X+a (a+1)X+a+1 X aX+a+1 1 (a+1)X+a (a+1)X+1 (a+1)X 1 X+a X+a+1 1 X+a+1 X 1 X+a aX+a 1 1 X X+1 1 1 a X+a+1 1 (a+1)X+1 aX+a+1 (a+1)X X+a aX+1 1 1 X+1 (a+1)X 1 aX+a+1 a aX+a+1 aX a+1 aX X+1 a+1 0 (a+1)X+1 X+a X+a aX+1 0 0 1 0 0 (a+1)X X 1 (a+1)X+a a+1 aX (a+1)X X aX aX (a+1)X aX+1 aX+a+1 a aX+a (a+1)X+a+1 (a+1)X+a X+1 a+1 X+a+1 aX+a 0 (a+1)X+a+1 X+a aX+a+1 X+a+1 X+1 aX 0 X+a+1 a+1 aX+1 0 X+a (a+1)X+a+1 (a+1)X+1 a X+a X+1 a+1 aX+1 (a+1)X+a+1 1 1 X (a+1)X+a+1 X+1 X+a 1 a aX+a+1 (a+1)X+a aX+a+1 a aX+a+1 1 a+1 aX aX+a aX+a aX 0 a aX+a aX aX (a+1)X+a aX+1 X+a+1 X+a X+a a X+a+1 (a+1)X+1 1 a+1 (a+1)X+a (a+1)X+a+1 aX (a+1)X+1 X+a+1 X (a+1)X+1 a+1 0 0 0 1 1 a (a+1)X+a+1 (a+1)X+a+1 a+1 X+a+1 aX+a+1 aX+a+1 aX+a+1 (a+1)X+1 1 (a+1)X+a aX+1 X+a aX aX+a X+1 (a+1)X+1 aX+a aX+1 (a+1)X X+1 X aX+1 a+1 (a+1)X+1 X+1 (a+1)X+a 0 a 0 aX a+1 X+a X+a+1 aX+a 1 X+a (a+1)X aX aX+a+1 (a+1)X+a+1 aX+a+1 (a+1)X+a a+1 1 (a+1)X+a+1 X X 1 X+1 X+a+1 (a+1)X+a X aX aX+a aX X+a 1 (a+1)X+a 0 X+a+1 a+1 (a+1)X+a X+a a+1 aX (a+1)X+a+1 1 (a+1)X+a aX+1 aX+a 1 aX+1 X+1 aX+a+1 (a+1)X aX (a+1)X+1 X+1 X+a+1 aX+a+1 0 a+1 (a+1)X+a generates a code of length 89 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 251. Homogenous weight enumerator: w(x)=1x^0+1392x^251+696x^252+4764x^255+1836x^256+6456x^259+2343x^260+8040x^263+2580x^264+8268x^267+2700x^268+7944x^271+2850x^272+6468x^275+1830x^276+3816x^279+1212x^280+1572x^283+300x^284+396x^287+33x^288+36x^291+3x^292 The gray image is a linear code over GF(4) with n=356, k=8 and d=251. This code was found by Heurico 1.16 in 87.2 seconds.