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

generates a code of length 58 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+318x^56+64x^57+256x^58+64x^59+318x^60+1x^64+2x^84

The gray image is a code over GF(2) with n=464, k=10 and d=224.
This code was found by Heurico 1.16 in 0.14 seconds.