The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+324x^57+141x^58+168x^59+93x^60+228x^61+17x^62+48x^63+1x^64+1x^70+1x^76+1x^82

The gray image is a code over GF(2) with n=472, k=10 and d=228.
This code was found by Heurico 1.16 in 82.3 seconds.