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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 X 1 1 1 1 1 1 1 0 X 0 0 0 0 X X X aX 0 X (a+1)X X (a+1)X (a+1)X (a+1)X aX X (a+1)X 0 (a+1)X aX X 0 aX X 0 0 (a+1)X (a+1)X (a+1)X (a+1)X 0 aX aX aX (a+1)X 0 aX aX 0 aX (a+1)X 0 aX X X 0 aX (a+1)X X X X 0 X X (a+1)X aX 0 X X aX X aX 0 aX (a+1)X aX X 0 (a+1)X 0 (a+1)X 0 0 aX aX aX 0 0 X aX (a+1)X X X (a+1)X 0 aX 0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX X 0 0 (a+1)X 0 aX aX aX aX (a+1)X (a+1)X X X 0 (a+1)X X (a+1)X 0 (a+1)X aX aX X 0 0 0 (a+1)X 0 aX aX X aX X X X X aX (a+1)X (a+1)X (a+1)X (a+1)X aX aX X X aX 0 aX (a+1)X 0 0 (a+1)X (a+1)X aX (a+1)X X aX X (a+1)X X X aX X X aX X 0 (a+1)X 0 X (a+1)X 0 (a+1)X 0 0 0 (a+1)X 0 0 0 X 0 (a+1)X 0 X aX (a+1)X X X X X 0 aX 0 aX 0 (a+1)X (a+1)X X X (a+1)X (a+1)X (a+1)X aX (a+1)X 0 aX aX aX (a+1)X aX X (a+1)X X (a+1)X X (a+1)X aX 0 (a+1)X 0 aX X X 0 aX aX X 0 aX aX aX X 0 (a+1)X 0 X X aX 0 aX 0 X 0 aX aX aX (a+1)X 0 0 0 X aX (a+1)X 0 0 aX (a+1)X 0 aX X X (a+1)X X (a+1)X X 0 0 0 0 X X X (a+1)X X X X aX 0 aX X (a+1)X (a+1)X aX aX 0 aX (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X aX aX aX 0 0 X X aX (a+1)X X X aX 0 aX (a+1)X X X X aX 0 (a+1)X 0 (a+1)X 0 0 (a+1)X aX 0 0 X aX (a+1)X 0 (a+1)X X 0 X (a+1)X aX X X (a+1)X aX X 0 (a+1)X (a+1)X 0 X (a+1)X aX 0 aX (a+1)X X X (a+1)X (a+1)X (a+1)X (a+1)X X aX 0 generates a code of length 89 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 252. Homogenous weight enumerator: w(x)=1x^0+105x^252+204x^256+153x^260+192x^261+132x^264+1152x^265+117x^268+1728x^269+60x^272+66x^276+42x^280+39x^284+21x^288+21x^292+21x^296+12x^300+12x^304+6x^308+3x^312+6x^316+3x^348 The gray image is a linear code over GF(4) with n=356, k=6 and d=252. This code was found by Heurico 1.16 in 0.376 seconds.