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

generates a code of length 59 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+34x^56+16x^57+28x^58+352x^59+28x^60+16x^61+34x^62+1x^64+2x^86

The gray image is a code over GF(2) with n=472, k=9 and d=224.
This code was found by Heurico 1.16 in 0.157 seconds.