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 X 1 1 X 1 X X 1 1 1 1 1 1 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 X a*X a*X X 0 0 a*X a^2*X 0 0 X a*X 0 0 a^2*X a*X a^2*X 0 a*X a^2*X X a*X X X X X a^2*X 0 a^2*X a*X X 0 X 0 a*X a*X a*X a*X X X a^2*X 0 X a^2*X X a^2*X X 0 0 a^2*X a^2*X 0 a^2*X X X 0 a*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 a*X a^2*X X X 0 X 0 a*X a*X 0 a^2*X a^2*X a^2*X a*X a^2*X a^2*X X X X X a^2*X X X X a^2*X a^2*X a*X a*X a^2*X 0 a*X a*X X 0 X 0 a*X X a*X 0 0 a^2*X a*X a^2*X a^2*X a^2*X 0 0 0 X a^2*X 0 0 0 a*X a*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 X a*X 0 X a*X a^2*X a*X a^2*X X a*X a*X a^2*X a*X a*X a*X a*X a^2*X a*X 0 0 0 0 0 a^2*X a^2*X X X 0 X 0 0 X a*X 0 0 a^2*X a^2*X a*X a*X a^2*X X X X a^2*X a^2*X a*X a*X X 0 X X X 0 X a^2*X a^2*X 0 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 X a^2*X X a^2*X X X a^2*X 0 a*X 0 X 0 0 X a*X X a*X a*X a^2*X a^2*X X 0 0 X a^2*X a^2*X a^2*X a^2*X a^2*X a^2*X X a^2*X a^2*X X a^2*X X a^2*X 0 a*X X a*X a^2*X a*X 0 0 a*X a*X X a^2*X X X a^2*X X a^2*X a^2*X a*X X a*X 0 generates a code of length 96 over F4[X]/(X^2) who´s minimum homogenous weight is 272. Homogenous weight enumerator: w(x)=1x^0+78x^272+210x^276+48x^277+159x^280+288x^281+141x^284+768x^285+72x^288+1248x^289+96x^292+720x^293+51x^296+48x^300+27x^304+42x^308+36x^312+21x^316+12x^320+6x^324+6x^328+3x^332+6x^336+6x^340+3x^364 The gray image is a linear code over GF(4) with n=384, k=6 and d=272. This code was found by Heurico 1.16 in 0.434 seconds.