The generator matrix 1 0 0 0 1 1 1 1 2X 1 2 2X 1 X 1 1 1 1 2 1 1 2X+2 0 X 1 0 1 3X 1 3X+2 X 1 0 1 1 1 1 3X+2 1 1 1 3X 3X+2 1 3X 1 2X 3X+2 2 2 2X+2 1 1 0 0 1 2 1 1 1 1 1 3X 2X 2X 1 3X+2 X 1 3X+2 X+2 3X 1 2X X 3X+2 1 1 1 1 1 1 1 1 1 3X+2 2 0 1 0 0 X 3 2X 1 1 3X X+2 1 3X+3 1 X+3 1 3X+1 2X+1 2 2 2X+2 1 X+2 1 2X 2X+2 0 1 1 1 2X+2 X+3 0 X+2 X 2X+3 X 1 X 3X X+3 1 X 1 3X+2 X+1 3X 2X+2 1 1 2 2 3X+2 1 1 X+1 1 2X+2 X+3 3X+2 X+1 1 1 1 X 3X+2 1 2X+2 3X+1 1 1 X+2 3 2X+2 2X+2 1 X+3 2X+2 3 2X X 3X 3X+3 2X+2 X+1 1 1 0 0 1 0 0 2X 2X+3 3 2X+3 3 1 X+3 2X+1 2 0 3X+3 3X+1 2 1 3X+1 X+2 X 3X 2X+3 X+1 1 2X 1 3X 2X 1 2 X+2 X+3 3X+2 2X+2 2X 3X X+1 X 1 3X+3 2X+2 0 1 3X+3 1 1 2X+3 1 X X X+2 0 2X+2 1 2X+1 X+3 3X+2 2X+2 3X 3X+3 X 2X+2 1 X+3 X 3X X+3 X+3 0 1 X+2 1 2 2X+3 3X 3X+2 X X 2X+1 2X+1 X+1 2X+1 X+2 2X+3 3X+3 0 0 0 1 1 3X+1 X+1 2X 3X+3 X 3 X 3 1 X+2 2 X+1 1 3X X+3 X 3X 1 3 2X+2 3 2X+1 3X X+2 X+1 3X+3 3 1 3X 2X 2 3X+3 X+1 2X+3 3 3X 3X+3 1 X+3 3X+3 1 2X+2 2X+2 X 1 1 3X+1 3X+2 2X+1 3X+2 2X+1 2X 1 X+2 X 3X+3 3X+2 1 2X+3 3 2 X 1 2X+3 3X+2 1 X+2 2 2 1 2X X 3X+2 1 2X+2 X+3 X+1 3 2 2X X+3 3 0 0 0 0 2 0 0 0 0 2 2 2X+2 2 2 2X+2 0 2X+2 0 0 0 0 0 0 0 2X+2 2 2 2X+2 2 2X+2 2X+2 2X 2X 2X+2 2X 2X 2X 0 2X+2 2X 2X 2X+2 2X+2 2 2X 2X 2X+2 0 2X+2 2X 2 2 2X+2 2X+2 2 2X 2X+2 2X 2X 0 0 0 2 0 0 2X 0 2X 2X+2 2X 2X 2X+2 2X+2 2X+2 2X 2 2X+2 2 2 2X 0 2X 2 2 2X+2 0 0 generates a code of length 87 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+562x^78+1640x^79+3685x^80+6544x^81+10730x^82+15652x^83+20996x^84+26588x^85+28634x^86+31280x^87+29665x^88+26800x^89+21658x^90+15712x^91+10037x^92+6036x^93+3042x^94+1532x^95+786x^96+264x^97+186x^98+36x^99+36x^100+8x^101+18x^102+4x^103+7x^104+2x^106+2x^108+1x^124 The gray image is a code over GF(2) with n=696, k=18 and d=312. This code was found by Heurico 1.16 in 821 seconds.