The generator matrix 1 0 0 0 1 1 1 1 2X 1 2X+2 2X 1 1 X 1 X+2 1 X 1 2X+2 1 X 3X+2 0 1 1 1 2X 1 1 2 2 1 1 1 1 1 3X 0 1 1 3X+2 2 1 1 1 X 3X 3X X 0 1 1 1 0 1 1 2 3X+2 1 1 1 2X 3X 1 1 1 X 3X+2 3X+2 1 1 1 X+2 1 X+2 1 0 1 1 1 1 1 1 X 1 0 1 0 0 X 2X+3 2X 2X+1 1 3X 3X+2 1 3X+3 3X+1 1 3X+2 1 2X+2 0 X+1 1 1 2X 1 1 1 X+1 X X X X+2 3X+2 1 2X 2X 2 1 X+2 1 1 2X+3 3X+1 2 1 3X+1 2X+3 3X+1 X 1 1 1 1 3X+1 2X 3X+2 1 X+1 3X+1 1 2 2X+3 X+3 3X+2 3X+2 1 3X+1 3X X+2 1 2 2 X+3 2X+2 2X 1 2X+1 1 3 1 1 3X 3X 2X+2 3X+2 3X 0 1 0 0 1 0 0 2X 3 2X+3 2X+3 2X+3 1 3X+3 2X+2 1 0 X+1 1 X+3 1 X+1 2X+3 1 1 3X 3X 2X+2 3X 2X+2 X X+3 2X 1 3 2X+1 3X+3 3X+2 X+2 3X+2 X+3 3X+2 2X+3 X+3 X+2 0 2 2X+3 3X 1 X+3 1 2X+3 2X 2X+3 2 2X+2 X+2 3X+1 1 X+1 1 X+3 3X+1 2X+1 1 X+2 2X+2 2X+1 3 3X+1 X 2 2X+3 X+3 1 2X+2 2X+2 2X+2 X+2 3X+1 2 2 3X 2X+3 3X+1 2X+1 1 2 0 0 0 1 1 3X+1 X+1 2X X+3 X 3 X 3X 2X+1 2X+3 2 3 X+1 3X 2X+3 X X+2 X+1 3X+3 X+2 2X X+3 3X 1 3X+3 3X+3 3X+3 1 2X+2 2X+1 3X+3 2X+3 3X 0 2X 2X+1 X+2 1 X+3 2X+2 2X+2 2 3X+1 3X 3 X+2 X+2 0 1 0 3 3X+1 3 2X+1 3 X+3 1 3 3X 3X X+1 2X 2X X+3 1 1 2X+2 X+3 3X+3 3 3X+3 3X+2 X+2 2 2X+3 1 0 3X+2 2X 3X+1 2 1 0 0 0 0 2X+2 0 0 0 0 2X+2 2X+2 2 2X+2 2X+2 2 2 0 0 0 2X+2 2 2X 2 2X+2 2X 2X+2 2X 0 2X 0 2X+2 2X+2 0 2X+2 0 2X+2 2X+2 2 0 2 2X 2X 2X+2 2X+2 2X 2 0 0 2X 2X+2 2 2X+2 2X 2X 2X 0 2X 2 0 2 2X 0 2X 0 2 0 0 2 2X 2X 2 2X+2 2 2 2X+2 2X+2 0 2X+2 2X 2X 2 2X 0 2 2X 2X 2X+2 generates a code of length 87 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+428x^78+1752x^79+3786x^80+6950x^81+10647x^82+15194x^83+20672x^84+25568x^85+29843x^86+31822x^87+29693x^88+27012x^89+21200x^90+15678x^91+10179x^92+5528x^93+3136x^94+1682x^95+744x^96+294x^97+177x^98+72x^99+45x^100+24x^101+4x^102+8x^103+4x^106+1x^118 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 790 seconds.