The generator matrix 1 0 0 0 1 1 1 1 X X+2 1 1 1 3X 2X+2 1 X+2 1 2X 0 X 1 1 X+2 1 2X 1 X 1 1 1 X 1 1 X+2 0 1 0 3X 2X 1 2 1 1 1 1 1 1 1 X+2 2 2X 1 1 1 2 1 X 1 3X+2 1 1 X+2 2 0 2 2X+2 3X 1 X 0 1 1 1 1 0 3X+2 3X+2 1 1 1 1 1 1 2X+2 1 1 1 2X+2 0 1 0 0 0 3 2X X+3 1 2 2X 3X+3 2X+3 1 1 2X+2 1 2X+1 2X 1 1 1 1 1 X 2X+2 X+1 X+2 3X X 3X+2 1 X+1 2 X+2 X X+2 1 1 3X+2 X+1 X+2 3X+1 2X+3 2 1 X+2 2X+3 X+3 1 1 1 0 X 1 2X+2 2X+2 1 2 X+2 3X 3 2X+2 1 X 1 2X 2 2 1 1 3 3X+1 3 X+1 X+2 3X 1 X+1 2X+1 3X+3 3X X+2 3 1 3 X+3 X+3 1 0 0 1 0 2X+2 2 3 1 3X+3 1 2X+1 X 2X+3 X X+3 2X+2 2X+2 3X+3 X+2 X+2 1 2X+2 0 2X+1 3X+1 1 X+3 1 X X+3 2X 3X 3X+3 2X 1 1 3 X+3 X+1 3X X 1 2X+2 2X+1 2X+1 3 X+2 X 2 X 2 3X+1 3X 2X+3 X+1 1 3X+1 3X+1 X+2 2 3 3X+3 1 1 1 2X+1 1 1 3X+3 2X+3 X+1 3X+2 X+3 2X+1 0 2X+2 1 3X+2 3 2X 2X+2 2X+2 3X+1 X 0 3X+3 2X+2 1 1 0 0 0 1 3X+3 3X+1 X+1 X+3 3X 3X+3 3X 2X 3X+2 3X+3 X+1 3X 1 0 1 2X+2 3X+2 3 X 2X+3 1 3X+1 1 X 3X 2 X+1 2X+1 X+2 2X+1 2X 2X+1 3X X+2 2X+3 1 2X+1 3X+2 3X X+3 2X+1 0 3X+1 1 2 3X+1 X 2X+2 2X 3X+3 X+3 2X+3 2X X+3 3X+2 1 3X+2 2X X+2 2X+2 3X+3 3X+1 X 2X+2 X 2X+3 2X+3 X 1 3 3X+3 1 X+3 2X+2 3X X+1 2X X+2 3X+2 X+3 3X+2 3X+3 X+2 2 3X+1 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 0 0 2X 0 2X 0 0 0 2X 2X 0 2X 0 2X 0 2X 2X 2X 0 2X 2X 0 0 2X 0 2X 2X 0 2X 0 0 0 0 0 0 0 2X 2X 2X 0 0 0 2X 0 2X 0 2X 0 0 2X 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 0 0 0 2X 2X 0 2X 2X 0 0 0 2X 0 0 0 generates a code of length 89 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+680x^81+1858x^82+3714x^83+5942x^84+8030x^85+10588x^86+13210x^87+14106x^88+15174x^89+14314x^90+13392x^91+10450x^92+8086x^93+5410x^94+2856x^95+1615x^96+916x^97+392x^98+182x^99+52x^100+34x^101+26x^102+22x^103+10x^104+6x^105+4x^106+2x^109 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 224 seconds.