The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 (a+1)X 1 (a+1)X 1 1 X 1 1 1 1 1 1 1 X 1 (a+1)X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 (a+1)X 1 X (a+1)X 1 1 1 0 0 1 1 1 1 1 1 (a+1)X 1 1 1 1 1 1 1 1 aX 1 1 1 0 1 1 0 1 1 1 X 1 1 1 1 aX 1 1 1 0 1 1 0 1 0 0 X aX 1 (a+1)X+a a+1 1 (a+1)X+a a+1 (a+1)X+1 (a+1)X+1 1 aX+a 1 aX+a+1 (a+1)X+a+1 1 a (a+1)X X+a+1 X+1 X+a aX+1 1 1 aX 1 aX a+1 (a+1)X X+a (a+1)X+a+1 a+1 (a+1)X+a X+1 X+a+1 X+1 aX+a X+a+1 aX+1 (a+1)X+1 aX+1 (a+1)X aX+a+1 1 (a+1)X+a+1 aX+a 1 0 1 1 0 X+a (a+1)X 1 X 0 X+a+1 (a+1)X+a+1 aX+a 1 aX+a+1 (a+1)X aX+a+1 (a+1)X aX+a aX+1 aX+a (a+1)X+a a aX+a+1 1 (a+1)X+1 (a+1)X+a (a+1)X+a+1 1 X+a+1 a 1 X+1 X+1 aX+a+1 1 a+1 (a+1)X aX+1 a 1 aX+1 0 (a+1)X+1 0 aX+a (a+1)X+a 0 0 1 1 (a+1)X+a (a+1)X+a+1 X+1 aX+1 (a+1)X+1 a+1 aX+a+1 X+a+1 a 0 aX+a aX+a (a+1)X+a+1 (a+1)X+a aX X+1 aX 1 aX+a+1 aX+a (a+1)X 0 (a+1)X+1 X a (a+1)X+a (a+1)X X a+1 a+1 (a+1)X+1 X+a aX aX+a 0 X+a+1 aX+1 X+a+1 aX+a X X+1 X+1 X (a+1)X+1 (a+1)X+1 (a+1)X+a (a+1)X+1 1 (a+1)X+a+1 a X aX+1 X+a 0 1 a X+a+1 (a+1)X+a (a+1)X+a+1 aX+a+1 a+1 1 X X+a+1 (a+1)X+a X+1 aX+a+1 a 1 aX+1 aX+a (a+1)X+a (a+1)X+a+1 X+a+1 (a+1)X+1 1 (a+1)X+a+1 aX+a+1 (a+1)X+a+1 X+a X+a (a+1)X+a X+a a+1 (a+1)X+1 X+a a+1 aX (a+1)X+a+1 aX 1 a (a+1)X 0 0 0 (a+1)X 0 0 (a+1)X (a+1)X (a+1)X 0 0 0 X aX (a+1)X X aX (a+1)X (a+1)X 0 0 0 (a+1)X (a+1)X (a+1)X (a+1)X aX (a+1)X aX X X X aX X X aX X 0 0 aX aX X aX 0 0 aX aX X aX 0 (a+1)X X (a+1)X aX aX 0 (a+1)X X aX X aX X aX (a+1)X aX X X X (a+1)X X 0 aX X X 0 aX (a+1)X 0 aX 0 X X (a+1)X 0 0 (a+1)X X (a+1)X (a+1)X (a+1)X 0 X 0 0 (a+1)X X (a+1)X generates a code of length 97 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 279. Homogenous weight enumerator: w(x)=1x^0+1128x^279+411x^280+2340x^283+885x^284+2304x^287+849x^288+1932x^291+690x^292+1596x^295+459x^296+1392x^299+303x^300+756x^303+228x^304+552x^307+216x^308+216x^311+36x^312+72x^315+18x^316 The gray image is a linear code over GF(4) with n=388, k=7 and d=279. This code was found by Heurico 1.16 in 16.3 seconds.