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 X 1 1 1 1 1 1 1 X X 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 X aX aX X 0 0 aX (a+1)X 0 0 (a+1)X aX X (a+1)X (a+1)X X aX aX aX 0 (a+1)X X aX (a+1)X aX (a+1)X (a+1)X (a+1)X (a+1)X 0 X X aX (a+1)X (a+1)X X 0 aX 0 0 (a+1)X 0 0 aX 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 aX (a+1)X X X 0 X 0 aX aX X (a+1)X X X X X aX X X aX 0 0 (a+1)X (a+1)X (a+1)X aX 0 aX aX (a+1)X X 0 (a+1)X (a+1)X aX aX (a+1)X 0 X 0 (a+1)X (a+1)X aX aX 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 X aX 0 X aX (a+1)X aX (a+1)X X aX X (a+1)X aX 0 0 (a+1)X (a+1)X 0 0 aX X aX X X aX X aX (a+1)X (a+1)X 0 (a+1)X X (a+1)X 0 aX (a+1)X 0 X X X (a+1)X (a+1)X X X 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 X (a+1)X X (a+1)X X X (a+1)X 0 aX 0 X 0 X aX 0 (a+1)X 0 (a+1)X aX (a+1)X X 0 aX aX (a+1)X (a+1)X (a+1)X aX 0 aX 0 (a+1)X X 0 X aX 0 X X aX (a+1)X X 0 0 generates a code of length 81 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 228. Homogenous weight enumerator: w(x)=1x^0+117x^228+183x^232+48x^234+168x^236+432x^238+135x^240+1296x^242+108x^244+1296x^246+63x^248+51x^252+39x^256+39x^260+33x^264+21x^268+24x^272+18x^276+12x^280+6x^284+3x^288+3x^312 The gray image is a linear code over GF(4) with n=324, k=6 and d=228. This code was found by Heurico 1.16 in 0.315 seconds.