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 X 1 1 1 1 1 1 1 aX 1 1 aX 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 aX+1 1 a+1 aX+a a+1 1 a+1 aX+a+1 X+a+1 a+1 X+1 aX+a+1 X+a+1 X aX aX 0 X (a+1)X 0 (a+1)X a+1 aX+1 (a+1)X+a X 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 a aX+1 0 a a+1 a+1 X+a+1 (a+1)X X+a aX+1 0 1 aX+1 (a+1)X 1 0 1 aX+a (a+1)X+a+1 (a+1)X+a+1 (a+1)X+a (a+1)X+a+1 a 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 aX+a+1 X+a+1 0 0 aX+1 a (a+1)X aX+a+1 aX a+1 aX a+1 (a+1)X+a (a+1)X+a+1 aX (a+1)X+a aX+a 0 0 X+a a X+1 X+a+1 X+a a+1 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+1500x^251+732x^252+4344x^255+1692x^256+6924x^259+2481x^260+7956x^263+2820x^264+7872x^267+2640x^268+8076x^271+2442x^272+6996x^275+2022x^276+3564x^279+1068x^280+1548x^283+372x^284+348x^287+105x^288+24x^291+9x^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 712 seconds.