The generator matrix 1 0 0 1 1 1 1 1 1 1 1 a^2*X 1 1 1 1 1 1 0 1 a*X 1 1 1 1 1 X 1 a*X 1 1 a^2*X 1 a*X X 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 X 0 1 1 1 1 1 X 1 1 1 1 1 a*X 1 1 0 1 1 1 a^2*X 1 1 1 X 1 1 1 1 a^2*X 1 1 a*X 1 0 1 0 0 X a^2*X 1 a^2*X+a a^2 1 a 1 a^2*X+1 a^2*X+1 X+a^2 a^2*X+a X+a^2 a 1 a^2*X+a^2 1 a^2*X+a^2 X a^2*X a*X+1 a^2*X+a^2 X X+1 1 0 a*X+a 1 a^2*X+a 1 1 X+a^2 a*X+a a^2*X+a^2 X+a^2 a*X+1 a^2 a a^2*X X+1 X+1 1 1 a^2*X+a a*X a^2*X+a^2 a 1 0 1 a*X X a X+a^2 a*X+1 a^2*X+a^2 1 a^2*X+1 X a^2*X+1 0 X+a 0 a^2*X+1 a^2*X+a 1 a X+a^2 a*X+a^2 0 a X+a X+1 a^2*X X+1 X+a a*X X+1 1 X+a X+1 1 a^2 0 0 1 1 a^2*X+a a^2 X+1 a^2*X+1 a*X+1 a^2 0 a*X+1 a X a^2*X a^2*X+a^2 X+a^2 a*X+a a a^2*X+a a*X+a^2 a*X+a a^2*X X+a^2 a a^2*X 1 0 a*X+1 a a*X+a a^2*X X a X+a^2 a*X+a^2 X+a^2 1 a^2 a^2*X+1 a^2*X+a a^2 X+a a*X+1 a^2*X+a^2 a*X+a a^2*X X+1 a^2*X+1 a^2*X a^2*X a^2*X+a^2 0 X+a^2 1 X+a^2 a^2*X+a X+a X+1 0 a^2*X+1 a*X+a a*X a*X a^2 a*X+1 1 a*X a^2*X+a 0 a^2*X+a^2 a*X+a 0 1 a^2*X+a^2 a X 1 X+a^2 X a^2*X a^2*X+a a^2*X+a X+1 a*X a^2*X+a^2 1 0 0 0 a^2*X 0 0 a^2*X a^2*X a^2*X X a*X X 0 a*X a*X X X a^2*X X a^2*X a*X X a^2*X a^2*X a^2*X 0 a^2*X a^2*X a^2*X a*X a*X a^2*X 0 0 X a^2*X 0 a*X 0 a*X a*X a^2*X X X a^2*X a^2*X a*X a*X X a^2*X X 0 a*X a^2*X X a*X 0 a*X 0 X 0 X X a*X X X 0 0 X a*X a*X 0 0 a*X 0 a^2*X X a^2*X a*X X 0 a*X a*X 0 X 0 X generates a code of length 87 over F4[X]/(X^2) who´s minimum homogenous weight is 249. Homogenous weight enumerator: w(x)=1x^0+552x^249+828x^250+360x^251+45x^252+1200x^253+1356x^254+492x^255+39x^256+1416x^257+1212x^258+456x^259+57x^260+1188x^261+1296x^262+348x^263+48x^264+1092x^265+852x^266+228x^267+27x^268+564x^269+660x^270+192x^271+12x^272+396x^273+396x^274+156x^275+15x^276+456x^277+240x^278+72x^279+12x^280+48x^281+72x^282 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 683 seconds.