The generator matrix 1 0 0 0 1 1 1 1 X+2 X^2+X+2 1 1 1 2 X 1 1 X^2+X+2 1 1 1 X+2 0 0 1 X^2+2 0 1 X 1 1 1 1 X 1 X^2+2 X^2+X+2 1 1 1 2 0 1 1 X^2+2 X+2 1 X^2 X+2 1 X X+2 1 X^2 2 X^2+X X^2+X 1 X+2 1 X^2 X^2 X^2 1 1 1 1 2 X 1 1 X^2+2 2 1 X^2 X+2 X^2+X 1 1 2 X^2+2 1 2 1 0 1 0 0 0 X^2+3 2 X^2+X+3 1 X^2 X+3 X^2+3 X^2+2 1 1 0 3 X^2+X+2 2 1 X^2+X+2 X^2 1 1 X+1 X+2 1 X 1 X^2+X 2 X^2+X+3 X+3 0 X^2+3 1 1 X X+3 X^2 X+2 1 X^2+X+3 2 1 1 X+3 X+2 1 X+3 X^2+X+2 X X+1 1 X+2 1 X^2 X^2+1 1 X^2+X 1 1 1 X^2+X X^2 X^2 X^2 X^2+X 1 X+3 X 2 1 X+1 1 1 1 X^2+3 3 1 1 1 X^2 X^2 0 0 1 0 X^2 X^2+2 X^2+3 1 X+1 1 X^2+1 2 X^2+1 X^2+X+1 0 0 X+1 1 X+3 X 3 1 X^2+3 3 X^2+X+1 X^2+X X+2 X+2 X+2 2 3 X^2+2 X+3 X+2 X+3 0 3 X^2+2 X+2 X+2 1 X^2 X^2+2 X^2 X+3 0 X^2+X 1 X+2 3 X 1 X^2+X+2 2 X^2+X+2 X^2+3 1 1 X^2+2 X^2+X+1 X^2+3 X X^2+X+2 X^2+3 X+1 X^2+X+1 X 1 3 2 X^2+X+1 0 X^2+2 X+1 X^2 X^2+X+3 2 X^2+X X X^2+X+3 X+3 X^2+2 2 X^2+X+2 0 0 0 1 X^2+X+1 X+3 X+1 X^2+X+3 X^2+X X+1 X^2+X 2 X^2 1 X^2+X+1 X+2 X^2 1 3 X^2+X+2 X^2+X 0 X 3 X^2+X+3 1 2 3 X+1 X^2+1 X^2+1 3 X 1 1 X+1 X^2+1 X^2+X 0 X^2 X+3 X^2+X+2 X+2 X^2+1 X^2+X+1 X^2+3 1 0 X^2+X X^2+1 1 X+3 X^2+X+3 X^2 1 X^2+X+3 X^2+X X^2 0 X^2+X+3 X+2 X^2+3 X+3 1 X+2 X^2 X^2+X+3 X X^2+X+2 X+1 X+3 1 X+1 3 X^2+3 0 X^2+2 X+3 X^2+1 3 2 0 1 X^2+2 0 0 0 0 2 2 2 2 0 0 2 2 2 0 0 2 2 0 2 2 2 0 0 0 2 0 0 2 0 2 2 2 2 0 2 0 0 0 0 0 2 2 0 0 2 2 0 2 2 0 2 2 0 2 2 2 2 0 2 0 2 2 0 0 0 2 0 0 0 0 2 2 2 0 2 2 0 2 0 2 0 2 2 2 generates a code of length 84 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+439x^76+1748x^77+3538x^78+5560x^79+7788x^80+11056x^81+13062x^82+14628x^83+15337x^84+15200x^85+13439x^86+10800x^87+7770x^88+5096x^89+2780x^90+1580x^91+692x^92+270x^93+133x^94+88x^95+35x^96+20x^97+8x^98+2x^101+2x^116 The gray image is a code over GF(2) with n=672, k=17 and d=304. This code was found by Heurico 1.16 in 201 seconds.