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

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+17x^56+40x^57+110x^58+688x^59+110x^60+40x^61+17x^62+1x^118

The gray image is a code over GF(2) with n=472, k=10 and d=224.
This code was found by Heurico 1.16 in 0.235 seconds.