The generator matrix

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

generates a code of length 63 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+122x^56+1018x^57+2214x^58+3940x^59+5257x^60+7334x^61+8962x^62+8556x^63+9092x^64+6684x^65+5141x^66+3596x^67+1787x^68+1182x^69+394x^70+172x^71+45x^72+22x^73+8x^74+8x^75+1x^82

The gray image is a code over GF(2) with n=504, k=16 and d=224.
This code was found by Heurico 1.16 in 32.7 seconds.