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

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

Homogenous weight enumerator: w(x)=1x^0+78x^56+352x^58+78x^60+1x^64+2x^84

The gray image is a code over GF(2) with n=464, k=9 and d=224.
This code was found by Heurico 1.16 in 0.156 seconds.