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 X aX 1 1 1 1 1 1 1 (a+1)X 1 1 1 1 1 0 1 1 1 aX 1 0 1 1 1 1 1 1 X 1 1 0 1 1 1 (a+1)X 1 1 1 1 1 0 1 1 1 1 aX aX 1 aX 1 1 1 (a+1)X 0 X X 1 1 1 X 1 1 1 0 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 (a+1)X+a+1 1 1 X+a (a+1)X X+1 X X+1 0 1 1 (a+1)X+a 1 a a+1 X+a+1 1 X+1 X aX+a+1 1 (a+1)X+1 1 (a+1)X+a+1 X+a aX+a X+1 (a+1)X+a+1 a+1 1 aX 1 X (a+1)X+a (a+1)X+a 0 1 aX+1 X+a a (a+1)X X 1 aX+a+1 (a+1)X aX X+a 0 X (a+1)X+1 1 (a+1)X+1 1 (a+1)X 1 1 1 1 aX+a+1 (a+1)X X+a 1 X+a+1 (a+1)X (a+1)X+a 1 (a+1)X+1 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 (a+1)X (a+1)X+a+1 aX+1 X+a+1 aX aX+a (a+1)X+1 aX (a+1)X+a+1 aX+a+1 0 (a+1)X+a aX+a+1 (a+1)X 1 a+1 (a+1)X 1 X aX (a+1)X+a 0 aX+1 aX+a+1 X+a X+1 aX+a a X+a aX+a+1 a X+a 1 aX+a+1 X+1 a+1 aX (a+1)X aX+1 (a+1)X a X+a+1 (a+1)X+a aX 1 aX+a X+1 1 1 a+1 aX+a+1 X+a+1 X+a+1 X+1 (a+1)X+a+1 0 aX+1 0 X+a (a+1)X+a (a+1)X+a+1 X+1 X+a aX+1 X+a+1 1 a 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 0 0 aX (a+1)X aX aX 0 aX aX X aX X X aX X aX X X X aX (a+1)X X aX 0 aX 0 aX X (a+1)X (a+1)X (a+1)X X (a+1)X 0 X (a+1)X X X aX aX (a+1)X 0 aX X aX X 0 aX (a+1)X X (a+1)X 0 0 0 X (a+1)X 0 0 0 (a+1)X X (a+1)X aX 0 X aX generates a code of length 88 over F4[X,sigma]/(X^2) who�s minimum homogenous weight is 252. Homogenous weight enumerator: w(x)=1x^0+561x^252+708x^253+396x^254+1494x^256+1200x^257+708x^258+1326x^260+1140x^261+528x^262+1149x^264+1104x^265+528x^266+921x^268+828x^269+456x^270+687x^272+528x^273+288x^274+540x^276+348x^277+108x^278+327x^280+240x^281+60x^282+132x^284+48x^285+30x^288 The gray image is a linear code over GF(4) with n=352, k=7 and d=252. This code was found by Heurico 1.16 in 2.31 seconds.