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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+6x^56+66x^57+105x^58+668x^59+105x^60+66x^61+6x^62+1x^118

The gray image is a code over GF(2) with n=472, k=10 and d=224.
This code was found by Heurico 1.16 in 0.125 seconds.