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 X 1 1 1 aX 1 0 1 1 1 1 1 X aX 1 (a+1)X 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (a+1)X (a+1)X 1 1 (a+1)X 1 X 1 1 1 X 1 1 aX 1 1 1 aX 1 1 aX (a+1)X 1 aX 1 1 1 1 1 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 1 (a+1)X+a+1 X+a X X aX+a 1 aX+a+1 X+a (a+1)X X X+1 1 0 X+1 1 X+1 aX+1 1 (a+1)X+a X+a+1 (a+1)X+1 a+1 a X+a+1 aX+1 (a+1)X+a+1 (a+1)X X+a X+1 a aX+1 aX+a+1 aX+a X+a+1 (a+1)X a+1 0 1 1 aX+a aX 1 (a+1)X+a+1 1 aX+a+1 (a+1)X+a+1 X+1 1 a+1 0 1 aX+a+1 aX+1 1 1 X+1 (a+1)X+a+1 1 1 aX+a 1 (a+1)X+a X+a (a+1)X aX+1 X+a (a+1)X+a 0 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 (a+1)X+1 X X aX+a 1 (a+1)X+1 aX+a (a+1)X+a a (a+1)X+a+1 aX+1 (a+1)X+1 (a+1)X+1 1 X+a aX+a aX 1 (a+1)X 0 a+1 (a+1)X+a+1 aX X+a+1 aX+1 a X+a+1 (a+1)X+a+1 X+a+1 aX+a+1 (a+1)X+a aX 1 aX a+1 1 0 X X+a X+1 X+1 a a+1 (a+1)X+a 0 (a+1)X+1 X+1 aX+a a+1 aX+a X X a+1 (a+1)X+a aX+a+1 (a+1)X+1 0 X X+1 (a+1)X+a+1 aX (a+1)X+a+1 aX+a+1 0 X+a X+1 (a+1)X+1 X a+1 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 aX 0 (a+1)X (a+1)X (a+1)X 0 X aX aX (a+1)X X aX (a+1)X aX (a+1)X 0 0 X X X aX (a+1)X (a+1)X (a+1)X 0 0 (a+1)X X X X 0 (a+1)X X aX X aX X X aX X X X X X aX aX 0 aX (a+1)X 0 (a+1)X 0 (a+1)X (a+1)X aX 0 X aX X 0 0 aX aX aX aX X (a+1)X X aX generates a code of length 87 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 249. Homogenous weight enumerator: w(x)=1x^0+588x^249+768x^250+324x^251+39x^252+1272x^253+1416x^254+540x^255+42x^256+1380x^257+1260x^258+432x^259+51x^260+1032x^261+1164x^262+360x^263+60x^264+1032x^265+960x^266+252x^267+36x^268+672x^269+684x^270+180x^271+3x^272+540x^273+360x^274+144x^275+15x^276+288x^277+240x^278+72x^279+6x^280+108x^281+60x^282+3x^284 The gray image is a linear code over GF(4) with n=348, k=7 and d=249. This code was found by Heurico 1.16 in 10.8 seconds.