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 1 X 1 1 1 1 1 1 0 0 1 1 a^2*X 1 a*X 1 1 1 1 1 1 1 1 a*X 1 1 1 1 1 a^2*X 1 1 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+a 1 X a^2*X+1 a^2*X+a a a^2*X+1 X+a X 0 a^2*X X+1 1 X+a 1 X+a X a^2*X a*X+1 a*X+a^2 a^2*X+a^2 X+1 X+a^2 1 X X+a^2 0 a*X+1 a*X+a^2 1 X+a a^2*X+1 X 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 a*X+1 1 a*X a^2*X+a a*X+a a^2 a*X+a a 1 1 X+1 a*X+a^2 a*X+a^2 a^2*X+1 a^2*X a*X a^2*X+a 1 a^2*X a*X+1 a^2*X+1 a*X+a^2 a^2*X+a a^2*X+1 X+a 0 X+a^2 a^2*X a^2 a^2*X+1 0 a*X+1 a^2*X+a^2 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 0 a*X X X 0 X a*X X X a^2*X a*X a*X 0 X a^2*X a^2*X a*X a^2*X 0 X 0 X X 0 a^2*X X X X a^2*X a^2*X a*X a^2*X a*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+468x^249+1152x^250+216x^252+1044x^253+1704x^254+210x^256+1212x^257+1968x^258+120x^260+1164x^261+1392x^262+213x^264+900x^265+1092x^266+147x^268+696x^269+780x^270+33x^272+336x^273+684x^274+66x^276+216x^277+396x^278+15x^280+108x^281+48x^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 57.2 seconds.