The generator matrix 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 2 X X 2 1 X 1 X 0 1 1 0 1 X 1 1 1 1 0 X 1 1 X 0 1 1 1 X 2 1 1 1 X 1 1 X 1 1 X 0 1 1 1 1 1 0 1 0 X 0 0 0 0 0 0 0 X+2 X X X X X+2 X+2 X 2 X 0 X 2 0 X+2 X 2 2 X 2 2 X X 2 X+2 X+2 X X X 0 2 0 0 X 2 0 X X X+2 2 0 0 2 0 0 X X+2 X+2 2 0 X+2 X X X+2 X 0 2 2 X X+2 X X X X X+2 0 2 0 X+2 X+2 2 X+2 X 2 X 0 0 0 0 X 0 0 X 0 0 0 X X+2 X 2 X X+2 0 0 X X+2 2 2 2 X 2 X 2 X X+2 X+2 0 X 0 X X 0 2 X 2 X+2 2 2 X+2 2 X X 2 0 X 2 X X+2 X+2 2 X X+2 2 0 X 0 X+2 X 0 2 X 2 X X+2 2 2 0 0 X 0 X+2 2 2 0 0 X X 0 2 X+2 X+2 X 2 2 0 X+2 X 2 0 0 0 0 X 0 X X X 0 X+2 2 X X+2 0 0 X+2 X+2 X+2 X X+2 0 2 2 X 0 0 X 0 0 X X 0 2 X+2 0 X 0 X 2 X X+2 2 X X 2 2 2 0 2 X+2 X+2 2 X+2 X 2 X X 2 0 2 0 0 X X X X 0 2 X X 2 X+2 2 2 0 2 X X X+2 2 0 X X X 2 2 X X 0 0 0 0 0 X X 0 X X+2 X 0 X 2 X+2 X 2 2 0 X+2 X 2 0 2 X 0 X X X X+2 2 0 X+2 2 0 0 X+2 X X+2 2 X+2 X X 2 2 X+2 X X+2 X+2 X+2 X X+2 X+2 X+2 2 0 X X X+2 X+2 2 X 0 0 0 X 0 X X X 2 0 0 X 2 X 2 2 X+2 X+2 0 X+2 2 X 2 X X X+2 2 X 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 2 0 0 2 0 0 2 2 0 2 2 2 0 0 2 2 2 2 2 2 0 2 2 2 0 2 0 2 0 0 0 2 2 0 2 2 0 0 2 0 2 0 0 2 2 0 0 2 2 0 2 0 2 0 2 2 0 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 2 0 2 2 2 2 2 2 0 0 0 2 0 2 0 0 0 2 2 2 0 2 2 0 0 2 2 0 0 2 0 2 2 2 0 0 0 2 2 2 2 2 2 2 0 2 2 2 0 0 0 2 0 0 2 2 2 0 2 0 2 0 2 2 0 0 0 0 2 2 0 2 0 2 generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+115x^78+318x^80+28x^81+463x^82+88x^83+626x^84+264x^85+794x^86+440x^87+885x^88+448x^89+856x^90+392x^91+749x^92+248x^93+484x^94+104x^95+284x^96+36x^97+242x^98+161x^100+97x^102+43x^104+19x^106+4x^108+2x^110+1x^136 The gray image is a code over GF(2) with n=356, k=13 and d=156. This code was found by Heurico 1.16 in 8.67 seconds.