The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+370x^56+1016x^57+2104x^58+2888x^59+3911x^60+4036x^61+4538x^62+4144x^63+3762x^64+2560x^65+1758x^66+912x^67+406x^68+156x^69+122x^70+24x^71+37x^72+8x^73+14x^74+1x^76

The gray image is a code over GF(2) with n=496, k=15 and d=224.
This code was found by Heurico 1.16 in 10.1 seconds.