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 1 1 1 0 1 1 X a^2*X 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 a^2*X a*X 1 1 1 1 a^2*X 1 1 0 1 1 1 1 1 1 1 1 1 1 1 X a^2*X 0 0 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 a^2*X a*X a^2*X+1 1 X+1 X+a 1 1 a*X+a^2 X+a^2 a^2*X a*X+a a*X X+a^2 1 X+1 a^2*X+1 1 0 a^2*X a^2*X+1 a^2 a^2*X+a X+a 1 1 a^2*X+1 X+1 a^2*X+a a*X+a 1 a*X+a^2 X+a 1 a^2*X+1 a X+a a^2*X+a a^2*X+a a^2*X+a 0 a*X+1 a^2*X a^2*X+a^2 a 1 1 1 0 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+a a*X+a^2 a^2*X+1 a^2*X+a X+1 X+a^2 a*X+a a^2*X a a*X+a a^2*X+a^2 1 a^2*X+1 a*X+a a*X+a a^2*X X+1 X+1 a^2 a*X+1 X a*X+a a^2*X+a^2 0 X+a a^2 a*X+1 1 a^2*X a^2*X+a^2 0 X a^2 X+a a^2*X a a a a^2 X+1 a^2 a*X+1 a^2*X+a^2 a^2*X X+1 0 X+a 1 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 X a*X X a*X a^2*X 0 a*X 0 0 X a^2*X a*X a^2*X a*X a*X a^2*X a*X 0 a^2*X a^2*X 0 0 X X a*X 0 0 a*X a^2*X a^2*X 0 a^2*X 0 0 a*X X a*X 0 0 a^2*X X 0 X a*X a*X X a^2*X X 0 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^2*X X a*X a*X a*X a^2*X X a*X a^2*X X X a*X a^2*X a*X 0 a*X a^2*X X a*X X 0 a^2*X X a*X 0 a^2*X 0 a^2*X X a^2*X a*X a^2*X X X 0 a*X 0 a^2*X a*X X a*X 0 a^2*X a^2*X X a^2*X a^2*X X generates a code of length 80 over F4[X]/(X^2) who´s minimum homogenous weight is 223. Homogenous weight enumerator: w(x)=1x^0+864x^223+480x^224+3252x^227+1332x^228+5520x^231+2022x^232+7704x^235+2853x^236+8952x^239+3111x^240+9492x^243+2778x^244+7392x^247+2157x^248+4176x^251+1230x^252+1560x^255+255x^256+240x^259+84x^260+24x^264+12x^268+12x^272+12x^276+15x^280+3x^284+3x^288 The gray image is a linear code over GF(4) with n=320, k=8 and d=223. This code was found by Heurico 1.16 in 42.3 seconds.