The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a^2*X a^2*X 1 1 1 1 0 X a*X 1 1 1 a*X 1 1 0 1 1 1 1 a^2*X 1 1 1 1 1 a*X 1 1 1 1 1 1 1 1 1 1 a*X 1 1 1 1 1 1 0 1 1 1 1 X 1 1 1 1 1 1 a^2*X 1 0 1 0 0 0 a^2*X 1 a^2*X+a a^2 a^2*X+1 a^2*X+1 a a^2*X+a^2 a^2 1 1 a^2*X+a 1 a^2*X+a^2 a 1 1 1 a^2*X+a^2 a^2*X X+a 1 X+a^2 a^2*X+a X a*X+1 a^2*X+a^2 a^2*X a*X 1 a 1 X+a^2 a*X+a^2 1 1 a a*X+1 a*X+1 a*X a^2*X+a^2 a^2*X a*X a a*X a*X+1 1 X+a a*X X+1 1 a^2*X+a a^2 1 X a*X+a X+a a*X+a^2 1 a X+1 X+a a*X+a a*X+a X 1 a*X+1 0 0 1 1 a a^2 1 X+1 1 a 0 X a*X+a a^2 X+1 a^2 X+a^2 a^2 0 X+a a X+a^2 X X+1 a^2*X+a^2 X X+a a 1 1 a*X+a X X+1 X X a^2*X+a a*X+a^2 a*X a*X+a^2 a^2*X+1 a^2 a^2*X+a a*X+a a*X a^2*X+a 1 1 a*X+a X+a^2 0 0 X+a a*X+a X+a^2 a^2*X+1 a^2*X+1 X+a^2 X a*X+1 a*X X+a a*X+1 a^2*X+1 X+1 a^2*X+a^2 a X a 1 1 a a 0 0 0 a^2*X 0 0 0 X X X a^2*X a*X a*X a*X a*X a^2*X a^2*X X a^2*X a*X X a^2*X 0 a^2*X X 0 0 X 0 a^2*X a^2*X a*X X a^2*X a*X a^2*X a*X X a^2*X X a*X a^2*X X a^2*X a*X a*X a*X X X a*X 0 a^2*X a^2*X a^2*X a^2*X X a*X X X 0 0 a^2*X 0 a*X a*X a^2*X a*X 0 a*X a*X 0 X 0 0 0 0 X a^2*X a*X X a^2*X a*X a*X X 0 a*X X a*X X a^2*X X a*X 0 0 a^2*X a^2*X X a*X a*X X 0 X X a^2*X 0 a^2*X a*X X a^2*X 0 a*X 0 a^2*X 0 X a^2*X a^2*X a*X a^2*X 0 a^2*X 0 X 0 a*X a*X 0 a*X a*X a^2*X a*X a^2*X a^2*X a^2*X X a^2*X a^2*X 0 0 0 0 X X a^2*X generates a code of length 72 over F4[X]/(X^2) who´s minimum homogenous weight is 199. Homogenous weight enumerator: w(x)=1x^0+372x^199+558x^200+276x^201+348x^202+1620x^203+1359x^204+924x^205+960x^206+3156x^207+2328x^208+1356x^209+1308x^210+4284x^211+3483x^212+1536x^213+1920x^214+5508x^215+3591x^216+1776x^217+1836x^218+5412x^219+3966x^220+1608x^221+1728x^222+4380x^223+2670x^224+1164x^225+900x^226+2052x^227+1116x^228+432x^229+192x^230+792x^231+276x^232+132x^233+24x^234+72x^235+30x^236+12x^237+24x^240+18x^244+15x^248+9x^252+9x^256+3x^260 The gray image is a linear code over GF(4) with n=288, k=8 and d=199. This code was found by Heurico 1.16 in 21.5 seconds.