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 1 1 1 a*X 1 a*X 1 1 1 1 1 a^2*X 1 1 1 a*X 1 1 X 1 1 X 1 1 1 1 1 1 1 a*X 1 1 1 1 1 1 1 1 1 1 1 1 1 a^2*X 1 0 a^2*X 1 1 a^2*X 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 X+a a^2*X+a^2 a^2*X+1 1 a^2*X+a^2 a 1 1 a*X+a a*X+a^2 0 X+a a^2*X+a^2 1 a*X a^2*X+1 X+a X 1 a^2*X+1 1 a^2*X+a a*X+1 X a*X a*X+1 1 X+1 a*X+a^2 X+1 1 a^2 X+a 1 a^2*X+a^2 1 1 a^2*X X a X+a^2 a^2*X a^2*X a^2*X+1 1 X+a^2 1 a^2*X+a X a*X+1 a*X+1 X+1 0 X+1 0 1 a^2*X+a a^2 1 1 1 1 X+1 a*X 1 a*X 0 0 a^2*X 0 0 0 X X X X X X a^2*X a^2*X a*X X a^2*X a*X a^2*X 0 a^2*X a^2*X a*X X 0 a*X 0 a*X 0 X a^2*X a*X a^2*X a^2*X X a*X a^2*X a*X a*X 0 a^2*X 0 a^2*X a^2*X a^2*X 0 a^2*X a*X 0 a*X X a*X 0 a^2*X a^2*X a*X a^2*X 0 a*X X 0 a*X a*X a^2*X a*X 0 a^2*X 0 a*X X 0 a^2*X a^2*X a*X X 0 a*X X a*X 0 a^2*X a*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 0 X 0 a*X a^2*X 0 a^2*X X a*X 0 X 0 a^2*X a*X a^2*X 0 0 a^2*X X X 0 a^2*X a^2*X a^2*X X a^2*X a*X X X X 0 a^2*X 0 a*X a*X X a^2*X 0 X 0 a^2*X a*X a^2*X a*X a*X X a*X a*X 0 X X 0 a^2*X 0 a^2*X a*X 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 X a*X a^2*X a^2*X 0 a^2*X a^2*X a*X a*X a^2*X 0 a^2*X a*X a^2*X a*X 0 a^2*X X a^2*X X X a*X 0 a^2*X X a*X a*X a*X a*X a*X a^2*X a*X a^2*X a^2*X 0 0 0 a^2*X 0 0 0 X a^2*X a^2*X a*X 0 a*X a^2*X a*X 0 a*X 0 a*X a^2*X a^2*X a^2*X 0 X 0 a^2*X a*X a*X a*X a*X X a^2*X generates a code of length 82 over F4[X]/(X^2) who�s minimum homogenous weight is 231. Homogenous weight enumerator: w(x)=1x^0+228x^231+288x^232+1296x^235+564x^236+1572x^239+600x^240+2208x^243+708x^244+2484x^247+678x^248+2592x^251+558x^252+1356x^255+405x^256+432x^259+132x^260+120x^263+60x^264+18x^268+21x^272+21x^276+18x^280+9x^284+6x^288+3x^292+3x^300+3x^304 The gray image is a linear code over GF(4) with n=328, k=7 and d=231. This code was found by Heurico 1.16 in 12.1 seconds.