The generator matrix 1 0 0 0 1 1 1 X^2+2 1 1 1 1 X^2 2 X^2+X+2 1 1 X^2+X 1 1 X 1 2 1 X^2 X X+2 1 1 X^2+2 1 0 1 X^2+X 1 1 0 1 1 1 1 1 X+2 1 X+2 X X^2+2 X^2+X+2 X^2+X 1 1 0 0 1 1 X+2 1 1 0 0 1 X+2 2 1 0 1 X^2+2 1 1 1 X^2 1 X^2+X X^2+X X^2+X 1 1 X^2 1 1 1 0 1 0 0 X X^2+1 X^2+X+3 1 X^2+X X+3 X^2 X^2+3 1 X 1 X+2 X^2 0 X+1 1 X^2+X X+3 1 X^2+X X 1 1 1 2 1 X+3 1 X^2+X+2 X^2 2 X^2+1 2 X 1 X+3 2 0 1 X^2+1 X^2+2 X 1 1 X^2+2 2 X+3 2 1 X^2+1 2 1 X 0 X^2 X+2 X^2+X+1 1 1 X+3 1 X^2+3 1 X^2+X X+2 X^2+X+2 0 X X+2 X^2+2 0 X^2+X+3 X^2+X+3 1 X^2+X+1 X+2 X^2 0 0 1 0 0 X^2 2 1 1 X^2+1 3 1 X+1 1 0 X^2 X^2+X+3 X^2 X^2+3 2 1 X^2+3 X+1 X 1 X^2+X+2 0 0 3 X^2+1 X^2+X+2 X^2+X X^2+1 1 X+2 X^2+2 1 X+2 X^2+1 X^2+X+1 X^2+2 X^2+1 X^2+1 X+2 X^2+X+2 1 X^2 X^2+3 1 X+2 X+1 1 X^2+2 X^2+X+1 X+1 X^2+X+3 X^2+2 1 1 1 X X^2+X+3 X^2+1 X^2+X+3 3 2 X^2+3 X+1 X^2+3 X^2+X+2 X^2+X+2 X+2 1 1 1 3 X^2+X+3 X^2 0 X^2+2 0 0 0 0 1 1 X^2+X+1 X+2 X^2+X+1 X^2+X X^2+3 X+1 2 X+2 1 X+1 X^2+X+1 X^2+1 1 X^2+X+3 X^2+X+2 X^2+X+1 X X^2+X+1 0 X^2+X+2 1 X^2+2 3 X+2 0 X^2+3 3 X^2+2 3 X+2 X^2 X^2+X X^2+X X^2+3 2 X^2+X+3 1 X^2+3 X+1 1 X^2+1 3 X X^2+2 X+3 X X^2 X^2+X X^2+1 X^2+X+3 X^2 2 2 X^2+X+3 2 X+1 X^2+X+1 X^2+X+1 2 X^2+3 X+2 X^2+2 2 0 X^2+X+1 1 X^2+X+2 X^2+2 X^2+X X^2+X+1 X^2 X^2+2 X^2+X+2 X^2+2 X^2+3 X+2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2+2 X^2 X^2 X^2 2 2 X^2 X^2 X^2+2 0 2 0 0 X^2 0 2 X^2+2 2 2 X^2+2 2 0 X^2 2 2 2 2 X^2 X^2+2 X^2+2 X^2 X^2+2 0 X^2 0 0 X^2+2 0 X^2+2 X^2+2 0 0 X^2 X^2+2 X^2+2 2 2 0 X^2 2 X^2+2 0 X^2+2 0 X^2 2 X^2+2 0 X^2+2 X^2 0 2 X^2+2 X^2+2 X^2+2 X^2+2 0 2 X^2+2 generates a code of length 81 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+317x^72+1362x^73+3459x^74+6200x^75+10227x^76+14438x^77+20674x^78+26286x^79+32065x^80+31744x^81+31746x^82+26664x^83+22208x^84+14916x^85+9286x^86+5302x^87+2857x^88+1280x^89+635x^90+266x^91+121x^92+34x^93+22x^94+14x^95+8x^96+2x^97+2x^99+4x^100+2x^102+2x^103 The gray image is a code over GF(2) with n=648, k=18 and d=288. This code was found by Heurico 1.16 in 684 seconds.