The generator matrix

 1  0  0  0  1  1  1  1 X^2+2  1  1  1 X^2+X+2  X X^2+X  X  1  1 X^2+2 X+2  1  1  1  1  1 X^2+2 X^2+X+2  0  1 X^2  1  1 X^2+X  1  X  0  1 X^2 X^2  1  1  1 X^2+2  1 X^2  2 X^2+X  1  1  1 X^2+2  1  1  1 X^2+X  1  1 X^2+X  1  1  1 X+2  1 X^2+2
 0  1  0  0  X X^2+1  3 X^2  1 X+3 X^2+X X+1  1  1 X+2 X^2+2 X^2+X+2  1 X^2+2  1 X^2+X+3  2  2 X^2+3 X^2+X+1  1  1  1  X X^2+X+2 X+1 X+2 X+2 X^2+1  0  1 X^2  1  1 X^2+1 X^2+2  0  1  X  1  1  0 X^2+X+2 X^2+X+3 X^2+X+1 X^2+X X^2  X  3  0 X^2+X+3  2  1 X^2+3 X+3  X X+2 X^2+X+1  1
 0  0  1  0  0 X^2  1 X^2+1  1 X^2+1  3  2  0  3  1  1 X+2 X^2  1 X^2+X+3 X+1  3  3 X+3 X^2+2 X+2 X^2+X+2 X^2+X+1  2  X X^2+3 X^2+X+3  1 X+3  2  3  X X+3 X^2+X+2 X^2+3 X^2+X+2 X^2+3 X^2+X+2 X^2+2 X^2 X+1  1 X^2+X  3  X  1 X^2+2 X^2+X+3  0  1 X^2+2 X^2+X+3 X^2+2 X^2 X^2+X X^2+X  1 X^2+1 X^2+1
 0  0  0  1  1 X^2+X+1 X^2 X^2+X+3 X^2+X+1 X^2+1 X^2+X+2 X^2+X X+1  2 X^2+3  0 X+1 X^2+X X^2+1 X^2  X  3  2 X^2+X+3 X^2+X+1 X^2+X+2 X+1 X+3 X^2+X+2  1 X^2+X+2 X^2  2 X^2+3  1 X^2+2 X^2+1 X^2+1 X^2+X+3 X^2+1 X+2 X+3  3 X+3 X+2 X^2+X+3  1 X+3 X^2 X^2+X+1 X^2+X X^2+1 X^2+X+1 X^2+1  3 X^2+3 X^2+2 X^2+X+2 X+2  X X^2+2  0  0  X
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2+2  2 X^2 X^2 X^2 X^2+2  0  2 X^2+2 X^2+2  2 X^2+2 X^2+2  2 X^2+2  2  0  2  0 X^2 X^2 X^2  0 X^2+2 X^2  2  2 X^2  0  2  0 X^2  0  0 X^2+2  2  2 X^2  0 X^2+2 X^2  2  0  2  2 X^2+2 X^2  2  2 X^2+2

generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+525x^56+1856x^57+4450x^58+8080x^59+13600x^60+20904x^61+28968x^62+33704x^63+36906x^64+34936x^65+29474x^66+21004x^67+13525x^68+7752x^69+3704x^70+1616x^71+764x^72+184x^73+144x^74+12x^75+18x^76+12x^78+4x^80+1x^92

The gray image is a code over GF(2) with n=512, k=18 and d=224.
This code was found by Heurico 1.16 in 691 seconds.