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

generates a code of length 58 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+156x^56+96x^57+104x^58+88x^60+32x^61+24x^62+7x^64+4x^72

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 0.171 seconds.