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 X 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1 1 X X 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^2*X a*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 X X a*X 0 X a^2*X a*X a*X a^2*X 0 X a*X 0 X 0 X 0 X X 0 a*X 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 a*X X 0 a^2*X a^2*X a^2*X 0 a^2*X 0 a*X X X X X 0 a^2*X X a*X a*X 0 a^2*X X 0 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 0 a^2*X a^2*X a*X X X a^2*X a^2*X X a*X a^2*X 0 0 0 0 X a^2*X 0 a^2*X X X 0 0 X X X X a*X a*X a*X a*X a^2*X 0 X 0 0 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 0 a^2*X a*X a^2*X 0 X a*X a*X 0 a*X a*X X 0 X a^2*X X a*X 0 X 0 a*X a*X a^2*X 0 0 0 0 X a*X a^2*X X X a^2*X 0 X 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 0 a^2*X 0 a^2*X 0 X 0 0 0 X X 0 a^2*X a*X X a*X a*X 0 0 a*X X a^2*X 0 a*X 0 a^2*X a^2*X a^2*X 0 0 a^2*X a*X a*X a^2*X 0 a^2*X X a*X a*X 0 a^2*X a*X a*X 0 a^2*X a*X a*X a^2*X a*X a*X a*X 0 generates a code of length 83 over F4[X]/(X^2) who´s minimum homogenous weight is 224. Homogenous weight enumerator: w(x)=1x^0+66x^224+285x^228+411x^232+60x^235+396x^236+420x^239+399x^240+1560x^243+414x^244+3720x^247+384x^248+4332x^251+297x^252+2196x^255+273x^256+267x^260+294x^264+189x^268+141x^272+96x^276+72x^280+54x^284+36x^288+15x^292+3x^296+3x^308 The gray image is a linear code over GF(4) with n=332, k=7 and d=224. This code was found by Heurico 1.16 in 3.91 seconds.