The generator matrix 1 0 0 0 1 1 1 1 3X X+2 1 1 1 X+2 X 1 2X 2X+2 1 1 0 1 3X 1 1 0 1 1 2X+2 1 3X+2 1 3X+2 2 1 1 1 1 2X X+2 2 1 3X 3X 0 0 1 1 1 1 1 X 1 X+2 2X+2 3X 1 1 1 1 2X+2 2X 1 1 3X 1 1 1 1 1 1 3X+2 1 1 1 1 0 1 1 1 X+2 2X+2 0 2 3X+2 1 X 1 1 0 1 0 0 0 2X+3 2X 3X+3 1 2 2 3 X+3 1 1 0 1 3X+2 3X+3 1 1 3X+2 1 2 3 2X+2 3 3X 1 2X+3 X X 3X 1 2X+2 X+1 3X+2 X+1 1 1 3X 3X+1 1 X+2 3X+2 1 2X+2 3X+2 X+3 X+1 1 1 3X 1 2 1 2X+3 X+3 3X+2 3X+1 2 1 X 3 1 0 2X+1 1 3X+1 X+2 3X+2 3X+2 3X+3 2 2X 2 X+2 0 3X X 1 1 2X 1 1 X+3 1 2X+3 X+1 0 0 1 0 2 2X+2 2X+3 1 X+3 1 2X+1 3 X X X+1 X 2X+1 1 X+3 3X X X+1 3 X+2 3X+3 1 3X 3 2X 1 2X 2X X X+3 X+1 3 X+3 X+2 3X 0 1 X 3 1 3X+2 3X+3 2X+2 0 2X 2X+3 0 0 2X+1 2 1 X 1 2X+1 2X+1 3X+2 X+2 3X+1 3X+1 1 3X+3 3X+3 3X+2 2X X+3 3X 2X+2 1 0 2X 3 3X+3 1 2 3X+1 X 2X+2 3X+1 1 0 2X+3 3 3X+3 2X+2 2X 0 0 0 1 X+3 3X+1 X+1 3X+3 X X+3 X+2 X+2 2X 3X+1 X+3 3X+2 1 X+1 3X+1 2X+1 3X X+1 2 3X+1 3X X+2 2X 0 1 2 1 X+1 1 3X+1 X+3 3 3X+2 X 2X+2 2X+3 2X+2 3X+3 3X+2 2X+3 1 X+2 3 2X 3X 0 3 X+3 X+2 X 3X+1 3X+3 X+3 X 3 2X+1 1 2X+1 X+3 3X+2 3X+1 1 3X 2X+2 3X+1 3X X+2 2X 2 X+2 2 2X+2 2X 2X+3 1 3X+3 0 0 2X+2 3X+2 1 X 2X 2X+2 X+1 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 0 0 2X 0 0 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 2X 0 0 2X 2X 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 0 0 2X 0 0 0 0 0 0 0 2X 0 0 0 0 2X 0 0 0 2X 2X 2X 2X 0 2X 0 0 generates a code of length 89 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+690x^81+1762x^82+3942x^83+5466x^84+8810x^85+10280x^86+12936x^87+13926x^88+15608x^89+14045x^90+13832x^91+9909x^92+8540x^93+5009x^94+3118x^95+1607x^96+874x^97+347x^98+198x^99+92x^100+36x^101+11x^102+22x^103+2x^104+5x^108+2x^109+2x^114 The gray image is a code over GF(2) with n=712, k=17 and d=324. This code was found by Heurico 1.16 in 217 seconds.