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 X 1 1 1 1 X 1 1 1 1 1 X X 1 1 1 1 1 0 X 0 0 0 0 X X X aX 0 X (a+1)X aX (a+1)X aX X X aX 0 (a+1)X aX X aX 0 X 0 (a+1)X aX X (a+1)X aX 0 0 aX aX X (a+1)X X (a+1)X (a+1)X 0 (a+1)X aX aX aX X 0 0 aX 0 (a+1)X (a+1)X 0 X X aX (a+1)X aX (a+1)X aX (a+1)X 0 aX (a+1)X 0 (a+1)X 0 aX X X X 0 aX X X 0 X (a+1)X X X 0 (a+1)X 0 (a+1)X 0 0 0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX aX 0 aX (a+1)X aX (a+1)X (a+1)X 0 X (a+1)X 0 (a+1)X 0 aX aX aX aX (a+1)X 0 (a+1)X (a+1)X 0 0 (a+1)X X X 0 aX 0 X aX X X X X aX X aX 0 (a+1)X aX X X aX X X X X (a+1)X aX X X 0 (a+1)X X 0 aX (a+1)X 0 X X aX 0 (a+1)X aX aX aX (a+1)X X X aX X (a+1)X 0 0 0 0 X 0 (a+1)X 0 X aX (a+1)X X X X 0 X (a+1)X X X (a+1)X (a+1)X (a+1)X aX 0 (a+1)X (a+1)X 0 X aX 0 (a+1)X 0 aX X X aX 0 aX 0 X (a+1)X 0 (a+1)X 0 aX X aX X aX X 0 (a+1)X 0 (a+1)X aX aX 0 X (a+1)X 0 X (a+1)X X 0 X (a+1)X X 0 (a+1)X X (a+1)X aX 0 aX aX 0 X 0 aX aX (a+1)X (a+1)X aX aX 0 X 0 0 0 0 0 0 X X X (a+1)X X X X aX 0 0 0 aX X aX (a+1)X (a+1)X aX 0 aX X aX aX 0 0 (a+1)X (a+1)X (a+1)X aX X 0 0 X aX aX X 0 aX X (a+1)X (a+1)X X (a+1)X (a+1)X X aX (a+1)X (a+1)X aX aX (a+1)X (a+1)X 0 X X aX X aX 0 aX (a+1)X 0 (a+1)X X aX aX X X X aX aX 0 (a+1)X 0 (a+1)X X 0 X 0 X 0 (a+1)X aX 0 generates a code of length 87 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 244. Homogenous weight enumerator: w(x)=1x^0+63x^244+162x^248+12x^249+168x^252+144x^253+138x^256+648x^257+93x^260+1296x^261+117x^264+972x^265+66x^268+39x^272+33x^276+42x^280+30x^284+27x^288+12x^292+15x^296+6x^300+3x^304+3x^308+3x^316+3x^332 The gray image is a linear code over GF(4) with n=348, k=6 and d=244. This code was found by Heurico 1.16 in 0.355 seconds.