The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+144x^57+556x^58+672x^59+670x^60+620x^61+344x^62+360x^63+235x^64+168x^65+184x^66+72x^67+52x^68+12x^69+4x^70+2x^76

The gray image is a code over GF(2) with n=488, k=12 and d=228.
This code was found by Heurico 1.16 in 0.234 seconds.