The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  X  X  X  1  1  1  X  1  X  X  X  X  1  1  1  1  X  X  X  X  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0 2X+2  0  0 2X+2  2 2X 2X  2 2X+2 2X 2X  2 2X+2  0 2X 2X+2  0 2X+2 2X+2  2  2 2X+2 2X  0 2X 2X+2  0 2X+2  2  2 2X+2 2X+2 2X  0 2X  0 2X  0  0 2X  2 2X  2  2  2  0 2X 2X+2  2  0  0 2X+2 2X+2  2 2X+2
 0  0  2 2X+2 2X 2X+2  2 2X 2X 2X+2  2 2X  0  2 2X+2  0  0 2X+2 2X+2  2  2  0  0 2X 2X+2 2X+2 2X  2  2 2X+2 2X  2 2X+2 2X  0 2X  2  0 2X+2  2  0 2X 2X  0  0  2 2X+2 2X  0 2X+2 2X+2  0 2X  2  0  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+23x^56+206x^58+23x^60+2x^74+1x^84

The gray image is a code over GF(2) with n=464, k=8 and d=224.
This code was found by Heurico 1.16 in 0.109 seconds.