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  2 3X+2  0 3X+2  2 3X  0 3X+2 3X  2  0 3X+2  2  X  0 3X+2  2 3X 2X X+2 2X+2  X  0 3X+2  2 3X 2X X+2 2X+2  X  0 3X+2  2 3X 2X X+2 2X+2 3X 2X X+2 2X+2 3X 2X X+2  2 X+2  0 3X+2 2X+2  X X+2 2X 2X+2 3X  X 3X+2  0
 0  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0 2X  0 2X  0  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X  0  0  0  0 2X  0  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0  0
 0  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0  0  0  0  0  0 2X  0  0 2X 2X 2X  0 2X  0  0  0  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+25x^56+72x^57+38x^58+752x^59+38x^60+72x^61+25x^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 0.187 seconds.