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 a*X 1 1 a^2*X 1 X 1 1 1 1 X 1 1 a^2*X 1 0 1 1 1 1 X 1 1 a^2*X 1 1 1 1 1 1 1 1 1 1 1 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 a*X a*X+a a^2*X+a^2 1 a^2*X+a^2 1 a^2*X a*X+1 X+1 a^2*X+a^2 1 X+a a 1 a^2*X+1 1 a^2*X a*X+1 a^2*X+a 1 1 0 X+a^2 1 a^2*X+a 0 a*X+a^2 a*X+a^2 a^2 X+a X+a^2 a*X+a 1 X+1 a*X+a^2 a^2*X+1 a^2*X+a 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 1 a^2*X+1 0 X+1 a^2*X+1 1 X+a^2 1 X+1 a*X+1 a a^2*X+1 1 a^2*X+a^2 1 X+a a^2 a*X+a^2 0 a^2 X+a^2 a^2*X+1 a^2*X+a^2 X a a^2*X+1 a*X+a a*X+a^2 X a^2*X+a^2 0 X+1 a^2*X a a^2*X+a a^2*X+1 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^2*X a^2*X+a^2 a*X+a a*X+1 X a*X+a X+a^2 X+1 a^2*X a*X+a a*X+a^2 1 X 0 a*X+a^2 1 a^2*X a^2*X 1 a^2*X+1 X+1 a*X+a a a*X+a^2 a*X+1 a^2*X+1 a^2 0 a^2*X a*X+a^2 X+a a*X+a^2 a*X+a^2 1 a 0 generates a code of length 76 over F4[X]/(X^2) who´s minimum homogenous weight is 212. Homogenous weight enumerator: w(x)=1x^0+348x^212+744x^213+780x^214+852x^215+1524x^216+1980x^217+1740x^218+1260x^219+2529x^220+2940x^221+2328x^222+1800x^223+3444x^224+3408x^225+2712x^226+2004x^227+3747x^228+3660x^229+2976x^230+1980x^231+3525x^232+3240x^233+2460x^234+1332x^235+2610x^236+2436x^237+1608x^238+1200x^239+1191x^240+1152x^241+672x^242+300x^243+483x^244+396x^245+84x^246+24x^247+51x^248+12x^249+3x^252 The gray image is a linear code over GF(4) with n=304, k=8 and d=212. This code was found by Heurico 1.16 in 23.9 seconds.