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 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 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*X+a a^2*X+a^2 X+a a^2*X 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 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 a^2*X+1 0 X a^2*X+a^2 0 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 X+a a^2 a 1 a*X+a^2 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+588x^215+552x^216+768x^217+720x^218+1968x^219+1581x^220+1728x^221+1392x^222+3060x^223+2775x^224+1992x^225+1848x^226+3516x^227+3468x^228+2352x^229+1908x^230+4116x^231+3270x^232+2460x^233+1860x^234+4416x^235+2805x^236+2340x^237+1812x^238+3108x^239+2019x^240+1392x^241+876x^242+1812x^243+1110x^244+648x^245+312x^246+456x^247+324x^248+108x^249+24x^250+12x^252+36x^253+3x^256 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 24.5 seconds.