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

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+87x^56+848x^58+87x^60+1x^116

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 0.234 seconds.