The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 X 1 1 1 a^2*X 1 1 1 1 a^2*X 1 1 1 a*X 0 1 1 1 1 1 1 a*X 1 1 1 1 1 1 1 1 X 1 1 0 a*X 1 a*X 1 1 1 1 1 1 1 a^2*X 1 X 1 1 1 X 1 0 1 X 1 1 1 1 1 1 a*X 0 1 1 1 1 0 1 0 0 a^2*X a*X a^2*X X X X 1 1 1 a a^2*X+a^2 a^2*X+a 1 X+1 a^2*X+1 X+a 1 a*X+1 a^2*X+1 X+1 a*X+1 1 a^2 a*X a 1 1 a*X+a^2 0 a^2*X+a X+a a*X+a 1 1 a*X+a^2 a^2*X+a^2 a*X+a^2 X X+a X+1 a^2 a 1 a*X+a^2 a^2*X+1 1 1 a*X a*X a*X+a a*X+a a^2*X+a^2 a^2*X X X+1 X X a^2*X+a 1 1 X+a X+1 1 a^2*X 1 a*X+a 1 a^2*X+a^2 a*X+1 a^2*X+a^2 a^2*X a*X+a^2 X 1 X 0 a*X a*X+a a^2*X+a 0 0 1 0 0 X X a^2*X+1 a a^2*X+a^2 a*X 0 a*X a*X X+1 a*X+a^2 a*X+1 X+a X+a X a*X+a a*X+1 a*X+a^2 1 X+a^2 X+1 a*X+a a*X+a a^2*X+a a*X+a^2 a^2*X+a^2 X+a^2 a^2*X+a^2 a^2*X+a X+a^2 a*X a X+1 a^2*X+1 X+a^2 a*X+a^2 1 1 0 a X+1 a*X a^2*X+a a^2 a^2*X+a a*X+a a^2*X+a 1 X+a X+a^2 X a*X+1 a^2*X+a a^2*X+a^2 X+a^2 1 X+a a^2*X+a^2 a a^2*X+1 a^2*X+1 X 1 1 a^2 a^2*X+1 0 X+1 X a*X+1 a^2*X X a^2*X+a^2 1 a*X+a X+a a^2*X+1 a*X+a^2 0 0 0 1 1 a^2*X+a a^2*X+a^2 a^2 X+a^2 a*X+a^2 a^2*X+a^2 X+1 a X a^2*X 1 0 X+a^2 a*X+a a^2 a^2*X+1 a^2*X a a^2 X a^2 a a*X+a a*X 1 a^2*X 1 a^2*X+a a^2*X+1 a*X+a^2 a^2*X+a a*X a*X+a a^2*X+1 a^2*X+a a^2*X a^2*X+1 X+a^2 a*X a^2*X+a^2 a^2*X+1 a^2 X+1 a^2 X a^2*X+a^2 a^2*X 1 a^2*X+a^2 a a*X+1 0 1 a^2*X+1 a*X a*X+a X+a a*X+a X+1 a a*X+1 a*X+1 a 1 a 1 a X+a a^2 X+a^2 0 a^2*X a^2*X+a^2 a^2 a^2*X+a^2 X+1 X a*X generates a code of length 83 over F4[X]/(X^2) who´s minimum homogenous weight is 233. Homogenous weight enumerator: w(x)=1x^0+792x^233+1200x^234+588x^235+75x^236+2244x^237+2520x^238+1104x^239+135x^240+3996x^241+4068x^242+1428x^243+138x^244+4392x^245+4752x^246+1524x^247+255x^248+4788x^249+4968x^250+1560x^251+174x^252+4584x^253+4788x^254+1488x^255+72x^256+3768x^257+3144x^258+816x^259+78x^260+2268x^261+1644x^262+528x^263+81x^264+720x^265+492x^266+168x^267+15x^268+96x^269+72x^270+12x^271 The gray image is a linear code over GF(4) with n=332, k=8 and d=233. This code was found by Heurico 1.16 in 48.7 seconds.