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 0 1 1 a*X 1 1 1 1 a^2*X 1 1 1 1 a^2*X 1 1 1 1 1 X 1 1 a*X 1 1 1 X 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 a*X 1 1 1 a*X 1 1 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 a^2*X+a^2 X+a a^2*X+1 1 a^2*X+a^2 a 1 0 a a^2 a^2*X+1 X+1 1 a^2*X a^2*X+1 1 a*X+a 0 a*X+a^2 X+1 1 a^2*X+a X+1 X+1 a*X+a^2 1 a*X+a^2 a*X a*X+a^2 a*X+a^2 X 1 a^2*X+a^2 X+1 1 a^2*X a*X a*X+a 1 a^2 1 a*X+1 a*X+1 a^2*X+1 X+a^2 a^2*X+1 a^2*X+a a^2*X+a 0 a*X a^2*X X+1 a^2*X+a a^2*X 1 a^2 1 a*X+a a*X+a a*X+a 1 a^2*X X+a 0 0 0 a^2*X 0 0 0 X X X X X X a^2*X a^2*X a*X X a*X a^2*X a^2*X 0 a^2*X a^2*X a*X a^2*X a*X 0 a*X X X a^2*X a*X a^2*X 0 a^2*X a*X 0 a*X a*X X a*X X a^2*X a^2*X a*X a*X 0 0 0 X X X X X a*X a*X 0 0 a^2*X a^2*X a*X a*X 0 a*X a^2*X a*X X X a*X 0 0 a^2*X a^2*X X a^2*X 0 a^2*X a^2*X 0 a*X 0 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 a^2*X 0 a*X a*X 0 a^2*X X X a*X X X 0 X a^2*X X 0 X X X a^2*X 0 a^2*X 0 0 a*X a*X X 0 a^2*X 0 a*X X a^2*X a^2*X X a*X 0 X a*X a^2*X a^2*X a^2*X 0 X a^2*X a^2*X 0 X a^2*X a^2*X a*X a*X a^2*X X X X 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 a*X X a^2*X a^2*X 0 a^2*X a^2*X X 0 a^2*X 0 a^2*X a^2*X a*X X X a*X X a^2*X X 0 a*X a*X 0 a^2*X a*X 0 X 0 a*X a^2*X X a*X X 0 a^2*X 0 X X a*X a^2*X 0 0 0 0 a*X a^2*X a*X X a*X X X a*X X a*X a^2*X a*X a*X a^2*X a^2*X 0 a*X X a^2*X generates a code of length 80 over F4[X]/(X^2) who´s minimum homogenous weight is 224. Homogenous weight enumerator: w(x)=1x^0+99x^224+204x^225+384x^227+477x^228+636x^229+672x^231+471x^232+804x^233+1020x^235+726x^236+1032x^237+1164x^239+669x^240+1212x^241+1272x^243+714x^244+1068x^245+1176x^247+567x^248+876x^249+396x^251+204x^252+240x^253+60x^255+42x^256+72x^257+42x^260+6x^264+21x^268+18x^272+15x^276+12x^280+9x^284+3x^288 The gray image is a linear code over GF(4) with n=320, k=7 and d=224. This code was found by Heurico 1.16 in 1.86 seconds.