The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1  1 3X  1  1  1  1  0 3X  1  1  1  1  1  1  1  1  1  1  1  1 2X  X  2 2X+2 3X+2 X+2  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 3X+2 X+1 2X+1  1  1  2 3X 2X 2X+2 X+2  X X+3 2X+3 3X+1  1 3X+3  3  1  1  1  1  1  1  0 2X X+2 X+2 2X 3X+2  2  X 2X+2  0  0
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0 2X  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X  0  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X  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+50x^56+288x^57+76x^58+192x^59+76x^60+288x^61+50x^62+1x^64+2x^86

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 0.109 seconds.