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 1 1 1 1 X 1 1 1 X X 1 1 1 1 X 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 0 (a+1)X aX aX 0 aX (a+1)X 0 aX X X 0 X X X aX X 0 X X (a+1)X (a+1)X X 0 aX aX (a+1)X aX (a+1)X aX (a+1)X (a+1)X X aX (a+1)X X X 0 X (a+1)X aX aX X 0 0 aX X X aX X X aX X 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 (a+1)X 0 0 aX aX X aX X X X X aX (a+1)X aX (a+1)X (a+1)X aX aX X X 0 aX 0 (a+1)X X (a+1)X X (a+1)X X aX X X 0 aX (a+1)X aX aX (a+1)X X 0 (a+1)X (a+1)X 0 (a+1)X aX 0 aX 0 0 0 (a+1)X aX 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 X (a+1)X (a+1)X aX 0 (a+1)X 0 aX X X 0 aX 0 aX aX aX 0 X X aX (a+1)X 0 X (a+1)X aX X (a+1)X (a+1)X 0 aX aX 0 aX 0 X 0 X (a+1)X aX (a+1)X (a+1)X 0 0 0 X 0 (a+1)X aX aX (a+1)X 0 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 0 aX aX (a+1)X X X X aX 0 (a+1)X 0 (a+1)X (a+1)X 0 aX 0 (a+1)X (a+1)X X 0 0 aX 0 0 0 X (a+1)X (a+1)X X aX (a+1)X aX 0 (a+1)X 0 X 0 (a+1)X X X 0 X X (a+1)X X X (a+1)X (a+1)X 0 (a+1)X 0 X X generates a code of length 90 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 256. Homogenous weight enumerator: w(x)=1x^0+267x^256+12x^258+144x^262+264x^264+648x^266+1296x^270+240x^272+972x^274+105x^280+57x^288+42x^296+24x^304+18x^312+3x^320+3x^344 The gray image is a linear code over GF(4) with n=360, k=6 and d=256. This code was found by Heurico 1.16 in 97.9 seconds.