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 1 a*X 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+a X+1 1 X+a^2 X+a 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^2 a^2*X a a*X X+1 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 X+a a*X+a a*X+a^2 X+a a^2 a^2*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+474x^224+1176x^225+480x^226+240x^227+1692x^228+3240x^229+1068x^230+336x^231+2643x^232+5508x^233+1464x^234+624x^235+3234x^236+5676x^237+1500x^238+480x^239+3399x^240+5904x^241+1704x^242+492x^243+3228x^244+5184x^245+1572x^246+492x^247+2709x^248+4464x^249+984x^250+324x^251+1458x^252+2040x^253+372x^254+84x^255+570x^256+564x^257+72x^258+36x^260+36x^261+12x^264 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 32.7 seconds.