The generator matrix

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

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+194x^56+182x^57+462x^58+296x^59+714x^60+614x^61+660x^62+272x^63+280x^64+146x^65+128x^66+8x^67+78x^68+18x^69+28x^70+12x^72+2x^74+1x^96

The gray image is a code over GF(2) with n=488, k=12 and d=224.
This code was found by Heurico 1.16 in 0.453 seconds.