The generator matrix 1 0 0 1 1 1 1 1 1 1 1 a^2*X 1 1 1 1 1 1 0 1 a*X 1 1 1 1 1 X 1 1 1 a*X a^2*X 1 a*X X 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 X 1 1 1 1 1 1 1 0 a*X 1 X 1 1 1 1 1 1 1 1 1 1 1 1 a^2*X a*X a*X 1 0 1 0 0 X a^2*X 1 a^2*X+a a^2 1 a 1 a^2*X+1 a^2*X+1 X+a^2 a^2*X+a X+a^2 a 1 a^2*X+a^2 1 X a^2*X+a^2 a^2*X a*X+1 a^2*X+a^2 X 0 X+1 a*X+a 1 1 a^2*X+a 1 1 X+a^2 a*X+a a^2*X+a^2 X+a^2 a*X+1 a^2 a a^2*X X+1 1 X+1 1 a^2*X+a a*X+1 0 X a^2*X+a^2 a*X a X+1 1 a^2*X+a^2 a*X a*X+a a*X+a^2 a X+1 a*X+a 1 1 a*X+a 0 a*X a*X+a^2 X a^2*X+a^2 a*X+1 a^2*X+1 a^2 a*X+a a^2*X+1 a*X+a^2 a^2 a^2*X+1 1 1 1 a^2*X+a 0 0 1 1 a^2*X+a a^2 X+1 a^2*X+1 a*X+1 a^2 0 a*X+1 a X a^2*X a^2*X+a^2 X+a^2 a*X+a a a^2*X+a a*X+a^2 a^2*X a*X+a X+a^2 a a^2*X 1 a 0 a*X+a a*X+1 a^2*X X a X+a^2 a*X+a^2 X+a^2 1 a^2 a^2*X+1 a^2*X+a a^2 X+a a*X+1 a*X+a a^2*X+a^2 a^2*X X+1 a*X+a^2 a^2*X+a^2 a*X+1 a^2*X 1 a^2*X a*X+a^2 X+a^2 a^2*X+1 X+1 a*X+1 a^2*X+a^2 a*X+a a*X+a a^2 a^2*X+1 a*X+a a*X+1 1 X+a X+a^2 0 X+1 a^2*X+1 X+a X X X+a a*X+a a*X+a 0 a*X+a^2 a^2*X+1 a^2*X+1 a^2 0 0 0 a^2*X 0 0 a^2*X a^2*X a^2*X X a*X X 0 a*X a*X X X a^2*X X a^2*X a*X a^2*X X a^2*X a^2*X 0 a^2*X a*X a^2*X a*X a^2*X a^2*X 0 0 X a^2*X 0 a*X 0 a*X a*X a^2*X X X a^2*X a^2*X a*X a*X 0 a*X a*X a^2*X X X a*X a^2*X 0 0 0 0 0 a*X a*X a*X a*X X a*X a*X a*X a*X 0 0 a^2*X X 0 X X a^2*X X 0 a^2*X a*X a*X generates a code of length 83 over F4[X]/(X^2) who´s minimum homogenous weight is 237. Homogenous weight enumerator: w(x)=1x^0+576x^237+684x^238+360x^239+42x^240+1284x^241+1344x^242+480x^243+51x^244+1212x^245+1500x^246+408x^247+48x^248+1164x^249+1200x^250+384x^251+48x^252+1056x^253+876x^254+312x^255+30x^256+852x^257+540x^258+168x^259+15x^260+420x^261+528x^262+144x^263+9x^264+252x^265+228x^266+24x^267+6x^268+96x^269+12x^270+24x^271+3x^272+3x^280 The gray image is a linear code over GF(4) with n=332, k=7 and d=237. This code was found by Heurico 1.16 in 31.2 seconds.