The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 a*X 1 X X 1 1 1 1 1 a*X 1 1 1 X 1 a*X 1 1 a*X 1 1 1 1 1 1 1 1 1 1 a^2*X 1 1 0 1 a^2*X a^2*X 1 1 1 a^2*X 1 1 1 1 0 X 1 1 a^2*X 1 X 1 a^2*X 1 1 1 0 1 0 0 a^2*X a*X a^2*X X X X 1 a^2*X+a a^2 a*X+1 X+a a^2*X+a a*X+a X+a X+a^2 X+1 a*X+1 a^2*X+a^2 a^2*X+a^2 a*X+a^2 a*X+a a^2*X+1 a^2 a*X a^2*X a*X+a 1 X+a^2 1 1 a^2*X+a^2 1 a^2*X a^2*X+a X+a 1 X+a^2 a*X a^2 1 a*X+a^2 1 a^2 0 1 a X+a 1 a*X+a a^2*X+a^2 1 X+1 X+a^2 X a*X+a^2 X a^2 a*X 1 0 0 1 0 a^2*X+a 1 1 a a^2*X a*X a^2*X+1 1 0 a*X+a^2 X+a^2 1 X+a 1 a*X 1 a*X+a^2 a*X+1 a*X+1 0 0 1 0 0 X X a^2*X+1 a a^2*X+a^2 a*X X a^2*X a*X+a^2 X+a a*X a^2*X X+1 X+a^2 a^2*X+1 a^2*X X+1 a^2 X+a a^2 X+a^2 a a*X+a a*X+1 a*X+a 0 1 a*X+a a^2*X+a^2 X+a a^2*X+1 a*X+a X+1 a*X+a^2 X+a a^2 a^2 1 X+a^2 a*X 1 0 a*X+a^2 X+1 a*X+a a^2*X+a a*X+a^2 a*X+a^2 a^2*X+a a^2*X+a a^2*X+a a*X a*X+1 X+a^2 1 a*X+1 a X X+1 1 a^2*X+a^2 X+a^2 1 a*X+a a^2*X+1 a^2*X+1 X+1 X X+a^2 a 1 0 a^2*X+a^2 X+a^2 a^2*X a*X+a a^2*X+1 a*X+a^2 a*X+a a^2*X+1 a*X+1 0 0 0 1 1 a^2*X+a a^2*X+a^2 a^2*X+a^2 a^2 a*X+a^2 X+a^2 X+a^2 X+a^2 a a^2*X+1 X a*X+1 a*X+1 X 1 a*X+a 1 X+a a^2*X+a^2 X+1 a*X a a a^2*X+1 a^2 X+a^2 X+a X+a a^2*X X+1 a*X+a a*X a^2*X a*X+a^2 0 X+a^2 a*X+1 a^2*X X+a^2 a a^2*X+a^2 a*X+1 X+a a 0 a*X+a a^2 0 a^2*X X a*X+a^2 0 a X+1 a*X+a^2 X+a X+a a a^2*X a*X+a a^2*X+1 X+a^2 a^2 a^2*X+1 1 a a*X+a^2 a a^2*X+a a*X+1 a^2*X+1 a^2*X+a^2 a*X+a X 1 a a*X+a a^2*X+a^2 0 a^2*X X+1 generates a code of length 86 over F4[X]/(X^2) who´s minimum homogenous weight is 242. Homogenous weight enumerator: w(x)=1x^0+1512x^242+852x^244+4224x^246+2181x^248+6708x^250+2460x^252+8172x^254+2562x^256+8424x^258+2964x^260+7728x^262+2658x^264+6612x^266+1716x^268+3996x^270+786x^272+1512x^274+168x^276+264x^278+33x^280+3x^288 The gray image is a linear code over GF(4) with n=344, k=8 and d=242. This code was found by Heurico 1.16 in 118 seconds.