The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1 2X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1 2X  X 2X+2
 0  X  0  X  0  0  X  X  2 X+2  2 X+2  2  2 X+2 X+2  0  0  X 2X  X  2  2 X+2 X+2  0  0  X X+2  2 2X  2 X+2  X 2X 2X+2 3X 3X+2 2X+2 2X 3X+2 3X 2X 2X+2 3X 3X+2 2X+2 3X+2 2X 3X 2X X+2 2X+2 2X 2X+2  X  X  X
 0  0  X  X 2X+2 X+2 3X+2  2  2 X+2 3X 2X 3X+2 2X 3X 2X+2 2X 3X+2 3X  X 2X+2 X+2 2X+2  0 3X+2 3X  2 X+2  2  0  X  X  X 2X 2X 3X 3X 2X  2 X+2 3X+2 2X+2  2 X+2 X+2  2  0 3X  X  2  0  0 3X+2 3X+2 2X+2 2X+2  2  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+243x^56+128x^57+320x^58+128x^59+172x^60+16x^62+15x^64+1x^104

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 0.484 seconds.