The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 X 1 1 1 1 1 X X 1 1 1 1 1 0 X 0 0 0 0 X X X a*X 0 X a^2*X a*X a^2*X a*X X X a*X 0 a^2*X a*X X a*X 0 X 0 a^2*X a*X X a^2*X a*X 0 0 a*X a*X X a^2*X X a^2*X a^2*X 0 a^2*X a*X a*X a*X X 0 0 a*X 0 a^2*X a^2*X 0 X X a*X a^2*X a*X a^2*X a*X a^2*X 0 a*X a^2*X 0 a^2*X 0 a*X X X X 0 a*X X X 0 X a^2*X X X 0 a^2*X 0 a^2*X 0 0 0 0 X 0 0 X a^2*X a*X a*X a*X 0 0 a*X a*X 0 a*X a^2*X a*X a^2*X a^2*X 0 X a^2*X 0 a^2*X 0 a*X a*X a*X a*X a^2*X 0 a^2*X a^2*X 0 0 a^2*X X X 0 a*X 0 X a*X X X X X a*X X a*X 0 a^2*X a*X X X a*X X X X X a^2*X a*X X X 0 a^2*X X 0 a*X a^2*X 0 X X a*X 0 a^2*X a*X a*X a*X a^2*X X X a*X X a^2*X 0 0 0 0 X 0 a^2*X 0 X a*X a^2*X X X X 0 X a^2*X X X a^2*X a^2*X a^2*X a*X 0 a^2*X a^2*X 0 X a*X 0 a^2*X 0 a*X X X a*X 0 a*X 0 X a^2*X 0 a^2*X 0 a*X X a*X X a*X X 0 a^2*X 0 a^2*X a*X a*X 0 X a^2*X 0 X a^2*X X 0 X a^2*X X 0 a^2*X X a^2*X a*X 0 a*X a*X 0 X 0 a*X a*X a^2*X a^2*X a*X a*X 0 X 0 0 0 0 0 0 X X X a^2*X X X X a*X 0 0 0 a*X X a*X a^2*X a^2*X a*X 0 a*X X a*X a*X 0 0 a^2*X a^2*X a^2*X a*X X 0 0 X a*X a*X X 0 a*X X a^2*X a^2*X X a^2*X a^2*X X a*X a^2*X a^2*X a*X a*X a^2*X a^2*X 0 X X a*X X a*X 0 a*X a^2*X 0 a^2*X X a*X a*X X X X a*X a*X 0 a^2*X 0 a^2*X X 0 X 0 X 0 a^2*X a*X 0 generates a code of length 87 over F4[X]/(X^2) who´s minimum homogenous weight is 244. Homogenous weight enumerator: w(x)=1x^0+63x^244+162x^248+12x^249+168x^252+144x^253+138x^256+648x^257+93x^260+1296x^261+117x^264+972x^265+66x^268+39x^272+33x^276+42x^280+30x^284+27x^288+12x^292+15x^296+6x^300+3x^304+3x^308+3x^316+3x^332 The gray image is a linear code over GF(4) with n=348, k=6 and d=244. This code was found by Heurico 1.16 in 0.356 seconds.