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 X X X X 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 X X X^2 1 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2 X^2 2 2 X^2 2 X^2 2 X^2+2 2 X^2 2 X^2 2 X^2 0 X^2+2 2 X^2 2 X^2 2 X^2 0 X^2+2 2 X^2 2 X^2 2 X^2 0 X^2+2 2 X^2 2 X^2 2 X^2 X^2+2 X^2+2 X^2+2 X^2 0 X^2+2 0 X^2+2 0 2 X^2+2 X^2 0 X^2+2 0 0 X^2+2 2 0 2 X^2 X^2+2 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 2 0 2 0 0 2 0 2 0 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 0 0 0 0 0 0 0 2 2 0 2 0 2 0 0 2 2 2 2 0 2 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 2 2 2 2 2 0 0 2 2 0 2 0 2 0 0 2 2 2 0 0 2 0 0 2 2 2 0 0 2 0 2 2 0 2 0 0 2 0 2 2 0 2 0 0 0 0 0 0 0 2 2 0 0 2 2 0 0 2 2 0 2 0 0 2 2 2 2 2 0 0 0 0 0 2 0 2 0 0 2 2 2 2 2 0 2 2 0 2 0 0 2 0 2 0 0 0 0 2 2 2 2 0 2 0 2 0 2 0 2 0 2 0 2 2 0 2 0 2 0 0 0 2 0 0 0 2 0 2 0 2 2 2 2 0 0 2 2 0 2 0 2 2 2 2 2 0 0 2 2 2 0 2 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 0 2 2 0 0 2 2 2 2 0 0 0 0 2 2 0 2 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 2 0 2 0 2 0 0 2 0 2 0 2 0 2 0 2 2 0 0 0 0 2 2 2 2 0 2 2 0 0 0 0 0 2 2 0 0 0 0 generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+22x^84+40x^85+22x^86+80x^87+150x^88+400x^89+148x^90+80x^91+18x^92+40x^93+17x^94+1x^96+3x^98+1x^110+1x^162 The gray image is a code over GF(2) with n=712, k=10 and d=336. This code was found by Heurico 1.16 in 0.844 seconds.