The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  X  X  X  1  1  1  X  1  X  X  X  X  1  1  1  1  X  X  X  X  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  0  2 X^2  0 X^2 X^2 X^2+2 X^2+2 X^2  2  0  2 X^2  0 X^2 X^2+2 X^2+2 X^2 X^2  2  0  2  0  2  0  0  2 X^2+2  2 X^2+2 X^2+2 X^2+2  0  2 X^2 X^2+2  0  0 X^2 X^2 X^2+2 X^2
 0  0 X^2+2 X^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 X^2 X^2+2 X^2+2  0  0  2 X^2 X^2  2 X^2+2 X^2+2 X^2  2 X^2+2 X^2  2  0  2 X^2+2  0 X^2 X^2+2  0  2  2  0  0 X^2+2 X^2  2  0 X^2 X^2  0  2 X^2+2  0 X^2+2 X^2+2 X^2

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+23x^56+206x^58+23x^60+2x^74+1x^84

The gray image is a code over GF(2) with n=464, k=8 and d=224.
This code was found by Heurico 1.16 in 0.125 seconds.