The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+81x^56+536x^57+884x^58+1220x^59+1230x^60+1176x^61+788x^62+800x^63+489x^64+408x^65+252x^66+172x^67+107x^68+40x^69+4x^70+3x^72+1x^76

The gray image is a code over GF(2) with n=488, k=13 and d=224.
This code was found by Heurico 1.16 in 0.672 seconds.