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 1 1 aX aX aX 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+1 a a+1 1 1 1 aX aX+a 1 (a+1)X+a+1 aX+1 (a+1)X 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 aX+a+1 X+a+1 X aX+1 (a+1)X X+1 X+a+1 0 (a+1)X+a+1 aX+a X 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 (a+1)X aX aX aX (a+1)X X aX 0 X (a+1)X X 0 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+528x^249+744x^250+396x^251+42x^252+1356x^253+1308x^254+504x^255+42x^256+1320x^257+1476x^258+396x^259+45x^260+1176x^261+1128x^262+276x^263+54x^264+948x^265+912x^266+264x^267+48x^268+684x^269+624x^270+300x^271+3x^272+456x^273+504x^274+120x^275+9x^276+312x^277+156x^278+24x^279+12x^280+108x^281+60x^282+24x^283+24x^285 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 324 seconds.