The generator matrix

 1  0  0  1  1  1 2X  1  1 3X+2  1  1 3X+2 X+2  1  1 3X  1 2X+2 2X+2  1  X  X  1  0  1  1  1  1  1  1  1  1 2X X+2 2X+2  1 2X+2 3X 3X  1  1  1  1 3X 2X+2  X  X  1  1  X 3X+2  1  0  1  1  1  2  2 2X+2  1
 0  1  0 2X+2  3 2X+3  1  0  2 2X X+3 X+1  1  1 3X+2 X+1 3X+2 3X+3  1  1  X  1  1  3  X X+2 X+1 2X+3 2X+1  0 3X+2 3X+3  2  1  1 2X 3X  1  0  1 X+3 2X+1 X+1  3  1  1 X+2  1 2X+2 3X+2  1  2  X 3X X+2 3X+2  0  1 3X+2  1  0
 0  0  1 3X+3 X+3  2 X+3 3X+2 2X+1  1 2X+3  2  0 X+3 2X 3X+2  1 X+1 X+2  1 X+1  3 X+2 2X+1  1  1 2X+3 X+2 X+1  X  X 3X 3X+3 3X  1  1  X 3X+3  1 X+1 X+1 X+2  2 2X 3X+3 2X+1  1  2  2  0 X+2  1 2X+2  1  3 X+3 X+3 2X  1  X  0
 0  0  0 2X 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X  0  0 2X  0  0  0  0 2X  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X  0 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+56x^56+554x^57+925x^58+1188x^59+1251x^60+1148x^61+815x^62+756x^63+469x^64+434x^65+298x^66+160x^67+77x^68+48x^69+9x^70+2x^72+1x^74

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 0.703 seconds.