The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a^2*X 1 a^2*X 1 1 1 0 1 a^2*X 1 1 1 1 1 1 a^2*X 1 a^2*X 0 1 1 0 X 1 1 1 1 1 a^2*X 0 1 a*X 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 X 1 1 a^2*X 1 1 1 0 1 1 1 a^2*X 1 1 1 0 1 0 0 0 a^2*X 1 a^2*X+a a^2 a^2*X+1 a^2*X+1 a a^2*X+a^2 a^2*X+a 1 a^2 1 1 a^2*X+a^2 a 1 X+a^2 0 a a a*X+1 X a^2*X+a 1 1 X+a^2 1 1 X a*X+a^2 1 X X+1 a*X+a^2 a^2*X a^2*X X+a^2 1 1 a^2*X 1 a*X+a^2 X+1 X X X 0 a^2 a^2*X+a^2 a^2 1 X+1 a^2*X+1 a a^2*X+a a*X+a 1 a^2*X+a X+a^2 1 a^2*X X+a^2 a 1 a*X+1 X X+1 1 X a*X+a^2 a*X 0 0 1 1 a a^2 1 X+1 1 a 0 X a*X+a a^2 a^2 a*X+a^2 X+1 a^2 0 a*X+a a a^2*X+1 1 X a*X+a^2 X 0 X+a a^2*X+1 a^2*X a^2*X+a^2 X+a^2 a^2*X+1 a^2*X+a X a 1 a^2*X+a^2 a X+1 a^2*X a*X+a a^2*X+a a^2*X+1 X+a^2 a^2*X X+a^2 a^2*X+a a^2*X+a^2 a a^2*X+a X+a^2 a^2*X+1 a^2*X X X+1 X+1 a^2*X+a^2 a^2 a X+a^2 a*X+1 0 a 0 a^2*X+1 X a^2*X+a a*X+a^2 a^2*X+1 X+a^2 a^2*X X+a^2 a*X+a 0 a*X 0 0 0 a^2*X 0 0 0 X X X a^2*X a*X a*X a^2*X a^2*X a*X a*X X a^2*X X a*X 0 X X a*X a*X 0 a*X 0 a*X X 0 a*X X X X X 0 0 a^2*X X X X a^2*X X a*X X a^2*X 0 a*X a^2*X a*X a*X a*X X X X X 0 a*X 0 a^2*X X a^2*X 0 a*X a^2*X 0 0 a*X 0 0 X 0 0 a*X 0 0 0 0 X a^2*X a*X X a^2*X a*X a*X X 0 X a*X a*X X a^2*X X a*X 0 X a^2*X a^2*X 0 a^2*X a^2*X a^2*X a^2*X 0 a*X a*X a*X X a*X a^2*X a*X a*X a^2*X a*X a^2*X a^2*X a*X 0 a*X a*X 0 a*X X a^2*X X X a^2*X a^2*X X X a^2*X X X 0 a^2*X a*X 0 0 X X a*X X a^2*X 0 0 X 0 a^2*X X a*X generates a code of length 76 over F4[X]/(X^2) who´s minimum homogenous weight is 211. Homogenous weight enumerator: w(x)=1x^0+576x^211+513x^212+2976x^215+1347x^216+5616x^219+2070x^220+8124x^223+2634x^224+9492x^227+3069x^228+9108x^231+2868x^232+7764x^235+2367x^236+3972x^239+1089x^240+1308x^243+282x^244+204x^247+63x^248+12x^251+24x^252+24x^256+21x^260+3x^264+3x^268+3x^276+3x^280 The gray image is a linear code over GF(4) with n=304, k=8 and d=211. This code was found by Heurico 1.16 in 27.6 seconds.