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 X 1 X 1 1 1 1 1 X 1 1 1 X X 1 1 1 1 1 1 1 1 1 1 1 1 0 X 0 0 0 0 0 0 0 0 0 a*X a^2*X a*X X a*X a^2*X a*X X 0 a*X 0 a*X X X a^2*X a*X a*X 0 a^2*X X a*X a^2*X X a*X a*X a^2*X a*X a^2*X X a*X 0 0 a^2*X a*X 0 a^2*X a*X a*X X 0 0 a*X 0 X X a^2*X X 0 X X a*X 0 a*X a*X X X a*X a^2*X X X X X 0 a*X 0 X a*X 0 0 a*X a^2*X 0 0 0 0 X 0 0 0 0 X X X a*X 0 a*X a*X a*X a^2*X 0 a^2*X a^2*X X X a*X 0 X 0 a*X a*X X X a^2*X 0 a^2*X a^2*X a*X X 0 0 0 X X a*X 0 X X a*X a*X X a^2*X a^2*X a^2*X a*X 0 0 a^2*X a^2*X a^2*X a^2*X X 0 X a*X a^2*X X a*X X a^2*X X 0 a^2*X 0 a*X X X X 0 a*X 0 0 X a*X X X a^2*X 0 0 0 0 X 0 0 X a^2*X a*X a*X a*X 0 a^2*X a*X a*X X a^2*X a*X a*X 0 a^2*X X a^2*X X a*X X 0 X a*X 0 X X X 0 0 X a^2*X a^2*X a*X a*X X 0 0 a^2*X 0 X a^2*X a^2*X 0 a^2*X a*X X X a^2*X a^2*X X a*X a^2*X 0 0 0 a^2*X a*X a^2*X a^2*X X a^2*X 0 X 0 a*X X X a*X 0 a*X a^2*X a*X X a*X a*X a^2*X 0 X 0 0 0 0 X 0 a^2*X 0 X a*X a^2*X a^2*X X 0 0 a*X 0 a*X 0 X a*X X 0 a*X X a*X X a*X X 0 a*X a^2*X a^2*X a^2*X X a*X a*X X 0 a^2*X X a*X X a*X a^2*X a^2*X X a^2*X 0 a*X a^2*X 0 X a*X a*X 0 a*X a*X X X 0 a*X a*X 0 0 0 0 a^2*X a*X X X 0 a*X a*X X X 0 0 a*X X a^2*X 0 0 a*X 0 0 0 0 0 X X X a^2*X X X a*X X 0 a*X a^2*X a^2*X a*X a*X a*X a*X a^2*X X a*X a*X a*X X a*X a*X a*X a^2*X a^2*X 0 0 a^2*X 0 X 0 0 0 X X 0 a^2*X a*X X a*X 0 a*X 0 a*X X a^2*X 0 a*X 0 a^2*X a^2*X a^2*X 0 0 a*X a*X a*X a*X X X X X a*X a^2*X a^2*X a^2*X a^2*X a*X 0 a^2*X 0 0 a^2*X 0 X 0 X generates a code of length 84 over F4[X]/(X^2) who´s minimum homogenous weight is 228. Homogenous weight enumerator: w(x)=1x^0+120x^228+318x^232+414x^236+12x^237+456x^240+180x^241+405x^244+1080x^245+330x^248+3240x^249+354x^252+4860x^253+330x^256+2916x^257+279x^260+288x^264+201x^268+210x^272+138x^276+84x^280+84x^284+39x^288+18x^292+24x^296+3x^316 The gray image is a linear code over GF(4) with n=336, k=7 and d=228. This code was found by Heurico 1.16 in 3.98 seconds.