The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+490x^56+968x^57+1710x^58+2016x^59+2337x^60+2040x^61+2346x^62+1448x^63+1300x^64+808x^65+474x^66+208x^67+132x^68+56x^69+26x^70+8x^71+3x^72+12x^74+1x^76

The gray image is a code over GF(2) with n=488, k=14 and d=224.
This code was found by Heurico 1.16 in 5.23 seconds.