The generator matrix 1 0 0 0 1 1 1 X^2 1 1 1 1 X^2+2 X X X^2+X 1 X^2+2 1 X+2 1 1 1 X+2 1 0 1 X^2+X+2 X 1 1 0 0 1 X+2 1 1 X^2+X 1 1 1 1 2 1 X 1 X^2 1 2 2 X+2 1 1 X^2+2 1 1 1 1 2 1 X^2 X^2+X+2 1 X+2 1 2 X^2+X+2 1 1 X^2+X+2 1 X^2+X X^2+X+2 1 1 1 X+2 X X X+2 X 1 0 1 0 0 X X^2+1 X^2+X+3 1 X^2+2 1 X^2+X+2 X^2+X+1 1 1 2 X^2+X+2 1 X X^2+X+3 X X^2+3 X+2 2 1 X^2+X+2 1 X+1 1 1 X X+1 1 1 X^2+2 2 X^2+X X X+2 1 X^2+X+3 X^2 X^2+X+2 1 X+3 2 X^2 X^2 X X+2 1 1 X^2+X+1 2 1 X 2 X^2+X 1 1 X^2+3 1 1 X^2+X 1 1 1 1 X+2 X^2 1 3 1 1 X+3 X+3 X^2+2 X^2+X+2 1 X^2+X 1 1 X^2+X 0 0 1 0 0 2 X^2 1 1 X^2+1 3 X^2+1 X+1 0 1 0 X+1 1 X+3 1 X^2 X X^2+X X+1 X^2+X+1 0 X^2+X X+1 X^2+X+2 X^2+3 X^2+X+3 X^2+X+2 X+1 X+1 1 2 X+2 1 X^2+1 X^2+X+2 1 X^2+2 X^2+2 X^2 1 X^2 X+2 X^2+X 1 1 X^2+3 X^2+X+2 X^2+3 X^2+2 X^2+1 X^2+X+3 1 X^2+X+2 X^2+X+2 X+3 0 X^2+2 X^2+X+2 X^2+2 1 X^2+3 3 2 X+2 1 X^2+X+2 X+1 X^2+2 X^2+1 3 X^2+X+1 1 X+2 1 X+1 X X^2+X 0 0 0 1 1 X+3 X^2+X X+1 X^2+X+1 X^2+2 X X^2+1 X^2+X+2 X^2+1 3 1 X^2+2 X^2+X+1 X^2+3 X^2 X^2+3 X+1 X^2 X^2+X+3 X+2 X^2+X 0 X X^2+1 X+1 X^2+X+1 0 X^2+1 X^2+X X^2+2 X+3 X^2 X^2+3 X X^2+X+1 1 2 X^2+X+1 2 X+1 X+3 1 2 0 X^2 0 X^2+X+1 0 X+2 X+1 X+1 X^2+X+2 X^2+2 X^2+3 X 1 X^2+X+2 X^2+X+1 3 X+3 X+2 2 2 X^2+X+3 X^2+3 3 2 X^2+X+3 X^2+X X+1 1 X^2+3 X^2+X+3 X+3 X+3 X^2+X X^2+2 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2+2 X^2+2 X^2+2 2 2 X^2 X^2+2 0 0 X^2+2 0 0 X^2 2 X^2+2 X^2+2 2 0 0 X^2+2 X^2 2 X^2 2 X^2 X^2+2 X^2 2 X^2+2 X^2 X^2 0 0 X^2+2 X^2 2 X^2+2 X^2+2 0 X^2+2 2 0 2 2 X^2+2 X^2 2 X^2 0 0 0 X^2 2 2 X^2 2 2 2 X^2 2 2 0 X^2 X^2 0 X^2+2 X^2+2 X^2 0 X^2 generates a code of length 82 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+272x^73+1605x^74+3354x^75+6209x^76+10176x^77+15076x^78+20922x^79+26300x^80+30350x^81+32751x^82+30458x^83+27873x^84+21104x^85+15347x^86+9828x^87+5265x^88+2796x^89+1326x^90+658x^91+252x^92+96x^93+59x^94+26x^95+16x^96+6x^97+6x^98+2x^99+2x^100+6x^102+2x^104 The gray image is a code over GF(2) with n=656, k=18 and d=292. This code was found by Heurico 1.16 in 697 seconds.