The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2+2 1 X+2 1 1 1 0 1 1 X^2+X X^2+2 1 1 1 1 X+2 1 1 0 1 1 X+2 1 1 X^2+2 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 X^2+2 1 1 X+2 1 X 1 X 1 1 1 1 1 1 1 X 1 1 1 X X 1 1 1 1 1 0 2 1 X^2+X X^2 1 X^2+X+2 1 X X^2 X^2+2 1 1 1 0 1 X+1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 X+2 1 3 X+1 0 1 X^2+X X^2+1 1 1 X^2+2 X^2+X+3 X+2 3 1 0 X+1 1 X^2+X X^2+1 1 X+2 X^2+X+3 1 X^2+2 3 1 0 X+1 1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 X+2 3 1 0 X^2+2 2 X^2 X^2+X X X^2+X 2 X^2+X+2 X^2 X+2 0 2 X+2 X^2+X+2 X^2+X X^2+X+2 X+1 X^2+X+3 X X^2+X X^2+2 1 1 X+3 1 X X^2+2 1 X^2+X+2 X^2+2 1 X X^2+1 X+1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 2 2 2 0 0 0 0 0 2 2 2 0 2 0 2 2 2 2 0 2 0 0 2 2 0 2 2 2 0 0 2 0 0 0 2 0 2 0 2 2 2 0 0 0 2 2 0 0 2 0 2 2 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 0 2 0 0 2 2 0 2 2 0 0 0 2 2 0 2 2 0 0 2 2 0 0 0 2 0 2 0 0 2 2 0 0 2 2 2 0 0 0 0 2 2 0 2 2 2 2 0 2 2 0 2 0 2 0 0 2 2 2 0 0 0 2 0 2 0 0 0 0 0 0 2 0 0 2 0 0 0 2 2 2 2 2 0 2 2 2 0 2 0 2 0 2 0 0 0 2 2 2 0 0 2 0 2 0 2 0 0 0 2 0 2 2 2 2 2 2 0 0 2 2 0 2 2 0 0 2 0 2 2 2 0 0 2 0 2 2 2 2 2 0 2 2 0 0 0 2 2 0 2 0 0 0 0 0 0 2 2 2 2 2 0 0 2 2 2 0 2 0 0 2 2 0 0 2 0 0 2 0 2 0 2 0 0 2 2 0 0 2 0 2 0 2 0 0 2 2 2 2 2 2 2 2 0 0 0 2 0 0 0 0 2 2 2 0 0 0 0 2 0 0 2 2 2 2 0 2 0 0 2 2 2 0 2 0 generates a code of length 84 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+44x^78+134x^79+381x^80+442x^81+396x^82+384x^83+631x^84+468x^85+327x^86+302x^87+292x^88+170x^89+55x^90+12x^91+32x^92+8x^93+7x^94+6x^96+1x^98+2x^110+1x^132 The gray image is a code over GF(2) with n=672, k=12 and d=312. This code was found by Heurico 1.16 in 0.687 seconds.