The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 X 1 1 a*X 1 1 1 1 1 1 0 1 a*X 1 1 1 1 a^2*X 1 1 1 1 a^2*X 1 1 1 1 1 X 1 1 a*X a^2*X 1 0 1 1 1 1 1 1 1 a^2*X X a^2*X 1 1 a^2*X 1 1 1 1 1 1 1 1 1 1 a*X 1 1 1 0 0 1 0 1 1 a a^2 0 a^2*X+1 a^2*X+a^2 a 1 0 a^2*X+1 a 1 a^2*X+a^2 X a^2*X+a^2 X+a a^2*X+1 1 a^2*X+a^2 a 1 0 a a^2 a^2*X+1 X+1 0 1 a^2*X+1 1 a*X+a a*X a*X+a^2 a*X+1 1 a^2*X+a 1 a*X+1 a*X+a^2 1 a*X+a^2 a*X a*X+a^2 a*X+a^2 a*X 1 a^2*X+a^2 X 1 1 a^2*X 1 a^2*X+1 1 a^2 X+1 a*X+1 a*X 1 1 1 1 a^2 a^2*X+a^2 1 a*X+1 a^2*X+1 a^2*X+a a^2 a*X+a a^2*X+a a^2 X X a^2 1 a*X+1 a*X+a^2 a*X+1 1 X 0 0 0 a^2*X 0 0 0 X X X X X X a^2*X a^2*X a*X X a*X a^2*X a^2*X 0 a^2*X a^2*X a*X a^2*X a*X 0 a*X X a^2*X X a*X a^2*X 0 a^2*X a*X X a*X a*X 0 a*X X a^2*X a^2*X a*X a*X 0 0 0 X X X a*X X 0 a*X X 0 0 a^2*X X X 0 X a^2*X a^2*X a^2*X a^2*X a*X X a*X 0 a^2*X a*X a*X a^2*X X a*X X a*X X a^2*X a*X 0 a^2*X 0 0 0 X 0 X a^2*X 0 X a^2*X X 0 a*X a^2*X 0 a^2*X 0 0 a*X a*X X X a^2*X a^2*X 0 a*X a*X 0 X a^2*X X a*X X X 0 0 a^2*X X X X X X a^2*X 0 a^2*X 0 0 a*X a*X a^2*X 0 a^2*X X a^2*X 0 X a*X 0 a*X a*X a*X a*X a*X a^2*X 0 a*X a*X a*X X X X a^2*X a*X a*X X 0 X a*X a*X 0 0 X a^2*X a*X 0 0 0 0 a^2*X a^2*X X a^2*X a*X 0 a^2*X X X a*X X a*X a*X X a^2*X a^2*X 0 a^2*X a^2*X X 0 a^2*X 0 a^2*X a*X a^2*X X X a*X X a^2*X a*X 0 a*X X 0 a^2*X a*X 0 X 0 a*X a^2*X X a*X a^2*X 0 X X a^2*X 0 X 0 0 0 a*X a^2*X a*X X 0 X X 0 X 0 a^2*X 0 a^2*X a*X 0 a^2*X X 0 0 a*X a*X a^2*X a*X a*X a^2*X generates a code of length 84 over F4[X]/(X^2) who´s minimum homogenous weight is 236. Homogenous weight enumerator: w(x)=1x^0+387x^236+1359x^240+2085x^244+2865x^248+2865x^252+3126x^256+2298x^260+1056x^264+183x^268+69x^272+21x^276+12x^280+18x^284+18x^288+9x^292+3x^296+3x^300+3x^304+3x^308 The gray image is a linear code over GF(4) with n=336, k=7 and d=236. This code was found by Heurico 1.16 in 1.97 seconds.