The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+86x^57+510x^58+852x^59+584x^60+634x^61+307x^62+472x^63+210x^64+148x^65+142x^66+64x^67+59x^68+16x^69+8x^70+2x^72+1x^82

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 0.203 seconds.