The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 X 1 1 X^2 1 1 X 1 0 X^2+2 0 X^2 0 0 X^2 X^2+2 2 0 X^2+2 X^2+2 2 0 X^2 X^2 0 X^2 X^2+2 0 X^2+2 2 0 X^2+2 0 X^2 X^2 0 2 X^2 0 X^2+2 2 X^2 X^2+2 2 2 X^2 X^2 0 2 X^2+2 0 X^2+2 2 2 X^2 X^2+2 X^2+2 0 0 X^2+2 X^2+2 0 2 2 X^2 X^2+2 X^2 X^2 2 0 X^2+2 2 2 2 X^2+2 X^2+2 2 X^2 0 0 2 2 2 0 X^2 2 2 X^2 X^2 2 X^2 X^2 0 0 X^2+2 X^2 0 X^2+2 X^2 0 X^2 0 X^2 2 X^2 0 X^2+2 2 X^2 X^2 2 0 X^2 X^2+2 2 0 0 X^2 0 X^2+2 X^2 X^2+2 2 2 2 2 X^2+2 0 X^2+2 0 X^2 X^2 0 X^2+2 X^2+2 0 2 X^2 X^2+2 0 X^2+2 2 X^2 0 X^2+2 2 X^2+2 X^2+2 0 0 2 X^2 0 2 X^2+2 X^2+2 2 0 X^2+2 X^2 X^2+2 X^2+2 X^2 X^2 X^2 2 X^2 X^2 X^2 X^2 X^2 X^2+2 X^2+2 2 X^2+2 X^2 0 0 0 2 0 0 2 0 2 2 0 2 2 2 0 2 0 0 2 2 0 0 2 2 0 2 0 2 2 2 0 0 0 0 0 2 2 2 2 2 0 2 0 0 2 0 0 0 0 0 0 2 2 2 0 2 2 2 0 0 0 2 2 2 2 2 0 0 0 2 2 2 2 0 0 2 0 0 0 0 2 0 2 0 0 0 0 0 2 0 2 2 2 2 2 0 0 0 0 2 2 0 2 2 2 2 0 0 0 0 0 0 2 2 2 2 0 2 0 2 0 0 2 0 0 2 2 2 2 2 0 0 2 2 0 2 0 0 0 2 0 2 0 2 2 2 0 2 0 2 0 0 2 0 0 2 0 0 0 2 2 0 2 2 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 2 0 2 2 2 0 2 2 2 0 0 2 2 0 2 2 2 0 0 0 2 0 0 0 0 2 2 2 0 0 0 0 2 2 0 2 2 2 2 2 2 2 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+50x^78+102x^80+32x^81+84x^82+480x^83+578x^84+480x^85+72x^86+32x^87+74x^88+44x^90+6x^92+6x^94+6x^96+1x^160 The gray image is a code over GF(2) with n=672, k=11 and d=312. This code was found by Heurico 1.16 in 0.797 seconds.