The generator matrix

 1  0  1  1  1 X+2  1  1 3X  1  1 2X+2  1  1 2X+2  1  1 3X  1  1 X+2  1  1  0  1  1  1  1 2X 3X+2  1  1  1  1  2  X  1  1  1  1  1  1  1  1 2X 3X+2  2  X  1  1  1  1  1  1  1  1 2X  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1 2X 3X+2 3X+1 2X+3  1  1  2  X X+3  1  1  1 2X 3X+2  2  X 3X+1 2X+3 X+3  1  1  1  1  1  0 X+2 2X+2 3X  0 X+2 2X+2 3X 2X  0
 0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X  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+22x^56+248x^57+22x^58+176x^59+8x^60+24x^61+8x^62+1x^64+2x^82

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 0.094 seconds.