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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+54x^56+64x^58+256x^59+94x^60+32x^62+9x^64+2x^84

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 0.172 seconds.