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  0  X 2X+2  X  0  X 2X+2  X  0  X 2X+2  X 2X  X  2  X  X 2X 2X  X  0  X  X  X  2
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 2X+2 3X  0 X+2 2X+2  X 2X 3X+2  2  X 2X 3X+2  2 3X 2X 3X+2  2  X 2X 3X+2  2 3X X+2  X 3X  X X+2  X 3X  X X+2  X 3X  X 3X+2  X  X  X X+2 3X+2  X  X 3X+2  X  X  X  0  0
 0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0 2X  0 2X  0  0
 0  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  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+124x^56+64x^57+104x^58+128x^59+80x^60+8x^62+1x^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 0.156 seconds.