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 1 1 1 1 1 1 X 1 1 1 1 1 X 1 1 1 1 1 1 1 0 X 0 0 0 0 X X X a*X 0 X a^2*X X a^2*X a^2*X a^2*X a*X X a^2*X 0 a^2*X a*X X 0 a*X X 0 0 a^2*X a^2*X a^2*X a^2*X 0 a*X a*X a*X a^2*X 0 a*X a*X 0 a*X a^2*X 0 a*X X X 0 a*X a^2*X X X X 0 X X a^2*X a*X 0 X X a*X X a*X 0 a*X a^2*X a*X X 0 a^2*X 0 a^2*X 0 0 a*X a*X a*X 0 0 X a*X a^2*X X X a^2*X 0 a*X 0 0 X 0 0 X a^2*X a*X a*X a*X 0 0 a*X X 0 0 a^2*X 0 a*X a*X a*X a*X a^2*X a^2*X X X 0 a^2*X X a^2*X 0 a^2*X a*X a*X X 0 0 0 a^2*X 0 a*X a*X X a*X X X X X a*X a^2*X a^2*X a^2*X a^2*X a*X a*X X X a*X 0 a*X a^2*X 0 0 a^2*X a^2*X a*X a^2*X X a*X X a^2*X X X a*X X X a*X X 0 a^2*X 0 X a^2*X 0 a^2*X 0 0 0 a^2*X 0 0 0 X 0 a^2*X 0 X a*X a^2*X X X X X 0 a*X 0 a*X 0 a^2*X a^2*X X X a^2*X a^2*X a^2*X a*X a^2*X 0 a*X a*X a*X a^2*X a*X X a^2*X X a^2*X X a^2*X a*X 0 a^2*X 0 a*X X X 0 a*X a*X X 0 a*X a*X a*X X 0 a^2*X 0 X X a*X 0 a*X 0 X 0 a*X a*X a*X a^2*X 0 0 0 X a*X a^2*X 0 0 a*X a^2*X 0 a*X X X a^2*X X a^2*X X 0 0 0 0 X X X a^2*X X X X a*X 0 a*X X a^2*X a^2*X a*X a*X 0 a*X a^2*X a^2*X a^2*X a^2*X a^2*X a*X a*X a*X 0 0 X X a*X a^2*X X X a*X 0 a*X a^2*X X X X a*X 0 a^2*X 0 a^2*X 0 0 a^2*X a*X 0 0 X a*X a^2*X 0 a^2*X X 0 X a^2*X a*X X X a^2*X a*X X 0 a^2*X a^2*X 0 X a^2*X a*X 0 a*X a^2*X X X a^2*X a^2*X a^2*X a^2*X X a*X 0 generates a code of length 89 over F4[X]/(X^2) who´s minimum homogenous weight is 252. Homogenous weight enumerator: w(x)=1x^0+105x^252+204x^256+153x^260+192x^261+132x^264+1152x^265+117x^268+1728x^269+60x^272+66x^276+42x^280+39x^284+21x^288+21x^292+21x^296+12x^300+12x^304+6x^308+3x^312+6x^316+3x^348 The gray image is a linear code over GF(4) with n=356, k=6 and d=252. This code was found by Heurico 1.16 in 0.373 seconds.