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 X X 1 1 1 1 1 1 0 X 1 0 1 a*X 1 1 1 1 1 1 1 1 1 a^2*X X 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 1 1 a^2*X+a X+a X+a 0 X+a a 1 1 a 1 X+1 1 X a*X+1 X X a X+a^2 1 a^2 a^2 a^2*X 1 X+a^2 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^2 X+a^2 1 a^2*X+1 a a^2 a^2*X+a^2 X X+a^2 a^2*X+1 0 X+a a*X+1 a*X+a^2 X+a^2 X+a a*X 1 a X+a^2 X+a^2 X a^2*X+a^2 1 0 a^2 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 a*X+1 a*X+a 0 a*X+a^2 X X a^2*X a^2*X X+a^2 X+1 a a X+a^2 a^2*X+1 a^2*X+1 a^2 X+1 0 a^2*X+a a*X+a X+1 0 a*X+1 0 a^2 a generates a code of length 77 over F4[X]/(X^2) who´s minimum homogenous weight is 215. Homogenous weight enumerator: w(x)=1x^0+480x^215+819x^216+696x^217+672x^218+1860x^219+1737x^220+1356x^221+1200x^222+3228x^223+2952x^224+1896x^225+1596x^226+4488x^227+3531x^228+2244x^229+1512x^230+4572x^231+3147x^232+2208x^233+1728x^234+4236x^235+3324x^236+1944x^237+1296x^238+3456x^239+2415x^240+1188x^241+876x^242+1740x^243+1182x^244+624x^245+312x^246+504x^247+330x^248+108x^249+24x^250+12x^251+15x^252+24x^253+3x^260 The gray image is a linear code over GF(4) with n=308, k=8 and d=215. This code was found by Heurico 1.16 in 23.9 seconds.