The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 a^2*X 1 1 a^2*X 1 X a*X 1 1 0 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 0 1 1 1 1 a^2*X 1 1 1 1 1 1 0 1 1 X 1 1 1 1 1 1 1 1 1 0 1 1 1 a^2*X 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 0 X a^2*X+a^2 X 1 X+a 1 1 a a^2*X+a 1 X X+1 1 a*X+1 0 a a*X+a^2 a*X+a a^2 a*X+1 1 a*X+a^2 a^2*X+a^2 X+a a^2 1 a*X+a a*X+1 a*X a*X+1 1 1 a^2*X X+1 a a*X+1 1 1 a^2*X+a X+a 1 1 X+a^2 a^2*X+1 a^2*X X a^2*X+a^2 a*X+a a^2 a^2*X+a 1 a a*X+a^2 X+a a*X a*X+1 a^2*X+1 0 a*X+a^2 a^2*X+a^2 a X+a^2 X+a a*X+1 X+a a*X+a^2 a^2*X+a^2 0 0 1 0 X a^2*X 0 a*X a*X a*X a^2*X+1 a^2*X+1 1 X+a^2 a*X+a^2 a^2 a*X+1 1 a^2 X+1 a a*X+a X+a X X+1 a 1 X+a^2 a*X+a^2 X a^2*X+1 X+a a a*X a*X+a a^2 X+1 a*X+1 a*X X+a^2 a*X+a^2 a^2*X+1 a^2*X+a^2 a^2*X+a^2 a^2*X+a^2 a X+a X+1 a^2*X X+1 1 a^2*X+a^2 X a*X+1 X a^2*X a a*X+a X+1 a*X+a a*X+a X+a a*X 1 a X 1 a^2*X+a a^2 a^2*X a^2*X a^2*X+1 a*X+a^2 a*X+a^2 a*X+a^2 a a*X+a 0 a*X+a 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^2 a^2 X a^2 a X+1 X+1 a*X+1 X+a X a^2 X+a^2 a*X+1 X a*X a*X+a^2 a*X+1 a a*X+a 0 X+1 1 a^2*X+a^2 a*X+a a^2*X+a a*X a*X a^2*X+a a^2*X+1 0 X+a^2 a*X+a X+a a*X+a X+1 a*X a*X+a a^2*X+a X+1 a*X+a X X a^2*X+a^2 X+a^2 a^2*X a^2*X 1 1 X+a a*X+a^2 X a^2*X a^2*X+1 a^2*X+1 a^2*X+1 a X+a a^2*X+1 a a*X a*X+a^2 a^2*X+a^2 X+a^2 a a^2*X a^2*X+1 a*X+a^2 a*X+1 a*X+1 a*X+1 generates a code of length 79 over F4[X]/(X^2) who´s minimum homogenous weight is 221. Homogenous weight enumerator: w(x)=1x^0+360x^221+924x^222+672x^223+993x^224+1332x^225+2028x^226+1596x^227+1734x^228+2304x^229+3180x^230+2460x^231+2088x^232+2964x^233+3576x^234+2304x^235+2505x^236+3012x^237+4068x^238+2412x^239+2265x^240+3060x^241+3420x^242+1980x^243+2082x^244+2076x^245+2484x^246+1608x^247+1161x^248+1392x^249+1392x^250+588x^251+417x^252+360x^253+384x^254+192x^255+57x^256+36x^257+48x^258+12x^259+6x^260+3x^264 The gray image is a linear code over GF(4) with n=316, k=8 and d=221. This code was found by Heurico 1.16 in 24.8 seconds.