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  2  X  X  X  X  X  2  X  X
 0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2  2  2  0 2X  0 2X  0 2X  0  0 2X  0  0 2X+2  2  2  2 2X  0 2X
 0  0 2X  0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X  0  0  0  0 2X 2X  0  0  0 2X
 0  0  0  0 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X  0 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  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+140x^56+256x^58+96x^60+17x^64+2x^80

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 0.312 seconds.