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 X^2 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 X 1 1 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 2 X^2 0 X^2+2 X^2 0 0 X^2+2 2 X^2 2 X^2+2 2 X^2 0 X^2+2 2 X^2 0 X^2+2 0 X^2+2 2 X^2 2 X^2 0 X^2+2 0 X^2+2 X^2 2 0 X^2 2 X^2+2 0 X^2 0 2 X^2 X^2 0 X^2+2 0 X^2+2 X^2 X^2 2 0 2 0 2 X^2+2 X^2+2 2 X^2+2 X^2 X^2+2 X^2 X^2 X^2 X^2+2 X^2 X^2+2 X^2+2 0 2 X^2+2 2 2 X^2+2 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 0 0 2 2 2 2 0 2 2 0 2 2 0 0 2 2 2 2 0 0 2 2 0 0 2 2 2 2 2 2 0 2 2 0 2 2 0 2 2 0 2 0 2 0 2 0 2 0 2 0 0 0 0 2 0 2 0 2 2 0 2 2 0 0 0 2 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 0 2 2 2 2 0 0 0 2 0 2 2 0 2 0 2 2 2 0 0 2 0 2 2 0 2 0 0 0 0 2 0 2 0 2 0 2 0 2 0 0 2 2 0 0 0 2 0 2 2 0 0 0 2 0 2 0 2 0 2 2 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 0 2 0 2 0 2 2 2 0 2 2 0 2 2 0 2 2 2 0 2 2 0 2 0 0 2 2 2 2 0 2 0 0 0 0 2 2 2 2 2 0 2 0 0 2 2 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 2 2 2 2 0 2 0 2 0 0 2 2 2 0 0 0 2 2 2 0 0 0 2 2 0 2 0 0 2 0 0 0 2 2 2 0 2 2 0 2 2 0 2 2 2 2 0 2 0 0 0 0 0 2 0 2 0 2 2 0 2 2 2 2 0 2 0 2 2 2 2 0 0 0 0 0 0 0 0 0 2 0 2 2 0 2 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 2 2 2 2 0 2 2 2 2 2 0 2 2 2 2 0 0 2 2 0 0 2 0 0 0 2 2 2 2 2 2 0 2 0 2 0 0 2 0 0 0 0 2 2 0 2 0 0 2 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+34x^78+142x^80+166x^82+256x^83+904x^84+256x^85+154x^86+64x^88+18x^90+40x^92+12x^94+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 0.813 seconds.