The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 a^2*X 1 1 1 a^2*X a*X 1 a^2*X 0 1 1 1 0 1 1 1 X 1 1 1 1 1 a^2*X 1 X 1 1 1 a^2*X 1 1 a*X a^2*X 1 1 1 1 1 a*X 1 1 1 1 1 a^2*X 1 1 a*X 1 1 X 1 1 1 1 1 1 1 1 1 a*X 1 1 a*X 1 1 1 1 0 1 0 0 a^2*X 0 a^2*X 1 a^2*X+a a^2 X 0 X X a^2*X+a^2 X+1 1 1 X+a 1 1 a^2*X+1 X a*X+1 1 a^2 a^2*X+1 X+a 1 a^2*X+a X+1 a X+a^2 a*X+a^2 1 a 1 a*X+a X+a^2 a*X+1 1 a X 1 1 a^2 a^2*X+a^2 a^2*X+1 a^2*X+a a*X+1 X a*X+1 0 X+1 a^2*X a^2*X+1 a*X a*X+a X+a 1 X+a^2 X 1 X+1 a^2*X+a^2 1 X+a^2 a a*X+a^2 a*X+a a*X+a^2 a^2*X 1 a^2*X+a^2 X+1 1 a^2*X+a^2 a^2*X+a a a^2*X+1 0 0 1 0 X a^2*X 0 a*X a*X a*X a^2*X+1 a^2*X+1 1 a^2*X+a X+a^2 X+1 X+1 1 a 1 X+1 a^2 a a*X+1 a^2*X+a a^2*X+1 a*X+1 0 a^2*X a*X+a^2 a^2*X+a a*X+1 a^2*X+a X+a a^2*X a*X a^2*X+a^2 X+a^2 a^2 0 a^2*X+a 1 X+1 a*X+a^2 a a*X+a 1 1 a*X+a a^2*X+a 1 a*X X+a a*X+a a^2*X+a^2 X 1 a^2*X+1 X+a^2 a*X a^2*X+a^2 a^2*X+a a*X+a^2 a*X 0 a*X+a^2 0 1 X+a^2 a 0 1 a^2*X+a^2 a*X+1 X+a^2 X+a a a^2*X+a a^2*X+a^2 X+a 0 0 0 1 a^2*X+1 a^2*X+a a^2 X+a^2 a^2*X+a^2 a*X+a^2 a^2 X a^2 a a a*X+a a*X a^2*X+a a^2*X+a^2 1 a^2*X+a^2 0 a*X a^2 a^2*X a*X+a X a X+a^2 X+a^2 1 0 a*X+a^2 a*X+1 X+1 a*X a^2*X X+1 a^2*X a*X+a a X+1 X+1 a*X+1 a^2*X+a^2 a^2*X 0 1 1 a^2*X X+a X+1 X+1 a^2*X+a 1 a*X+a 0 a a^2 a^2*X+a a*X+1 a^2*X+a^2 a*X+a^2 0 a*X 1 X+a^2 a*X+1 a^2*X+a^2 a*X+a a^2*X+1 a*X+a X+a^2 a*X+a^2 a^2*X+a a*X a a^2*X a*X+a a*X+a^2 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+558x^224+900x^225+804x^226+192x^227+1668x^228+2568x^229+1776x^230+384x^231+2898x^232+4536x^233+2064x^234+516x^235+3549x^236+4956x^237+2160x^238+648x^239+3765x^240+4596x^241+2472x^242+552x^243+3333x^244+4332x^245+2148x^246+408x^247+3024x^248+3624x^249+1608x^250+252x^251+1611x^252+1740x^253+624x^254+96x^255+498x^256+360x^257+156x^258+24x^259+87x^260+36x^261+12x^262 The gray image is a linear code over GF(4) with n=320, k=8 and d=224. This code was found by Heurico 1.16 in 28 seconds.