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 X 1 1 1 1 1 1 X 1 X 1 1 1 1 1 1 X X 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 X 0 a*X 0 a^2*X a^2*X a^2*X 0 X X X 0 0 0 X X a*X X 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 a*X X a^2*X a^2*X X a*X X a^2*X a^2*X a*X X X a^2*X a^2*X a*X 0 X 0 0 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^2*X a*X a^2*X a*X a*X 0 0 a^2*X 0 X a*X X a*X X a^2*X a^2*X a*X 0 0 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^2*X a^2*X 0 a^2*X 0 a^2*X 0 X X 0 X a^2*X X 0 a*X a^2*X a^2*X X generates a code of length 86 over F4[X]/(X^2) who´s minimum homogenous weight is 244. Homogenous weight enumerator: w(x)=1x^0+147x^244+36x^247+213x^248+288x^251+135x^252+840x^255+144x^256+1152x^259+87x^260+756x^263+84x^264+36x^268+39x^272+33x^276+27x^280+9x^284+21x^288+18x^292+12x^296+12x^300+3x^304+3x^324 The gray image is a linear code over GF(4) with n=344, k=6 and d=244. This code was found by Heurico 1.16 in 0.516 seconds.