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  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
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X  0 X^2+X+2 X^2  X X^2+2  X  0 X^2+X  0 X^2+X+2 X^2  X X^2+2  X  0 X^2+X  0 X^2+X+2 X^2  X X^2+2  X  2 X^2+X+2 X^2 X+2  2 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X X^2+2 X+2  2 X^2+X X^2 X+2  2 X^2+X+2 X+2 X^2  2  2
 0  0 X^2+2  0 X^2+2 X^2  0 X^2  2  2 X^2 X^2+2 X^2 X^2+2  2  2  0  0 X^2+2 X^2 X^2 X^2+2  2  2  2  2 X^2 X^2+2 X^2+2 X^2  0  0  2  2  2  2 X^2 X^2+2 X^2 X^2+2  0  0  0  0 X^2+2 X^2 X^2 X^2+2 X^2+2 X^2  2  0 X^2  0 X^2  0  2  0
 0  0  0  2  2  0  2  2  0  2  0  0  2  2  2  0  2  0  2  2  0  0  0  2  2  0  2  2  0  0  0  2  0  0  2  2  0  0  2  2  0  0  2  2  2  2  0  0  0  0  0  0  2  2  0  0  2  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+87x^56+848x^58+87x^60+1x^116

The gray image is a code over GF(2) with n=464, k=10 and d=224.
This code was found by Heurico 1.16 in 0.25 seconds.