The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 1 a^2*X 1 1 1 1 1 1 1 1 a^2*X 0 1 1 1 1 1 1 1 1 X 1 1 1 X 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 a*X 0 a*X 1 1 1 1 1 a^2*X 1 0 1 a*X 1 1 1 1 1 1 1 1 1 X 1 a^2*X a^2*X 1 1 0 1 0 0 a^2*X 0 a^2*X 1 a^2*X+a a^2*X+1 X+1 X+1 a*X+a^2 1 X+a^2 a^2*X+a^2 a*X a*X+1 a*X+a^2 1 X+a^2 a*X a^2*X 1 a^2*X a^2*X+1 a 0 a*X+a^2 X+a^2 a*X a^2*X+a 1 a^2*X+a a^2*X a*X+1 a^2*X 1 X+a X+a^2 a*X+a^2 a a*X+1 a^2*X+a^2 a^2 0 a a*X+a^2 0 a^2*X+a^2 X+a X+a a^2*X+a^2 a X+a 1 1 a*X a^2*X+a a*X a^2*X+a a^2*X+a 1 1 X+1 1 0 1 a^2*X+1 a X+1 a^2 X+a a^2*X a*X a^2*X+a^2 X 1 a 1 1 a^2 0 0 0 1 0 X a^2*X 0 a*X a*X a^2*X a^2*X a*X X a 1 X+a a^2*X+a^2 X+a a X+1 X+a^2 a^2 1 X+1 a^2*X+a a^2 a^2*X+a 1 a^2*X+a^2 X+1 a*X+1 a^2*X+a^2 0 X+a^2 X+a a^2*X+a 1 a*X+a X+a^2 a^2 1 a*X+a a*X+a^2 a^2*X 0 a 1 a^2*X+a X+1 a^2*X+1 X+1 a 0 a*X+a^2 a^2*X+1 X X+a^2 1 1 a^2*X+1 0 a*X+a^2 X+a^2 a*X+1 a*X+1 a*X+a^2 a a a X+a X+a^2 X+a X+a a^2 a*X X+a a*X+1 X a*X X+a^2 X+a a*X+a^2 X 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 a^2*X a*X+1 a a*X+1 a*X+a^2 a*X+a^2 X X+1 X+a a*X 0 X+a^2 X+a a^2*X+a^2 X+a a a*X+1 X+a X+1 a^2*X+a a^2 a^2*X+1 a^2*X+a^2 X+a a^2*X+a^2 a 1 a^2*X a^2*X+a^2 a^2*X+a^2 a*X a^2*X+a^2 a*X+a^2 a^2*X+1 X a*X X+a^2 1 a^2*X+1 a*X+1 a*X+1 X a^2*X+a^2 0 X+a 1 X+a^2 a^2*X+a^2 0 a*X a*X 1 X a^2*X a^2*X+1 X+a X+1 a*X 1 0 a*X+1 a*X X+a a a*X a^2 1 a^2*X a*X+a X+1 a*X+a^2 a^2*X+a 0 generates a code of length 83 over F4[X]/(X^2) who´s minimum homogenous weight is 232. Homogenous weight enumerator: w(x)=1x^0+279x^232+264x^233+432x^234+984x^235+1617x^236+1380x^237+1248x^238+1932x^239+2775x^240+1956x^241+1884x^242+2736x^243+3882x^244+2016x^245+2028x^246+2928x^247+3777x^248+2508x^249+2280x^250+2820x^251+3831x^252+2304x^253+1944x^254+2676x^255+3024x^256+1920x^257+1476x^258+1680x^259+2328x^260+1032x^261+708x^262+912x^263+840x^264+348x^265+264x^266+228x^267+174x^268+84x^269+24x^270+12x^273 The gray image is a linear code over GF(4) with n=332, k=8 and d=232. This code was found by Heurico 1.16 in 26.5 seconds.