The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2+2 1 1 X+2 1 1 0 1 1 X^2+X 1 1 X^2+2 1 1 X+2 1 1 1 1 0 X+2 1 1 1 1 1 1 2 X X^2+2 X^2+X X^2 X^2+X+2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 X+1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 X+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+X X+1 3 1 1 X^2+2 X+2 2 X^2 X^2+X+2 X 1 1 1 1 1 1 X^2+X+3 X^2+X+1 1 X+3 X^2+1 X^2+3 0 2 X^2+X+2 X^2+X+2 2 X^2+2 X^2+X X+2 0 0 0 2 0 2 0 2 0 2 2 0 2 0 0 0 2 0 0 2 2 2 0 2 2 2 0 0 2 2 0 0 2 2 0 2 0 2 0 0 2 0 2 0 2 0 2 0 2 2 2 0 0 0 0 2 0 0 0 0 0 2 2 2 2 0 0 0 2 2 2 2 2 2 0 0 0 2 2 0 0 0 2 0 0 2 0 2 2 2 0 0 0 2 2 0 0 2 2 0 2 0 0 2 2 0 0 2 2 0 2 0 0 2 0 generates a code of length 57 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+24x^54+296x^55+102x^56+176x^57+102x^58+296x^59+24x^60+1x^64+2x^82 The gray image is a code over GF(2) with n=456, k=10 and d=216. This code was found by Heurico 1.16 in 0.109 seconds.