The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  2  X X^2+2
 0  X  0  X  0  0  X  X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X  0  0  X  2  X X^2 X^2 X^2+X X^2+X  0  0  X X^2+X X^2  2 X^2 X^2+X  X  2 X^2+2 X+2 X^2+X+2 X^2+2  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  2 X^2+X X^2+2  2 X^2+2  X  X  X
 0  0  X  X X^2+2 X^2+X X^2+X+2 X^2 X^2 X^2+X X+2  2 X^2+X+2  2 X+2 X^2+2  2 X^2+X+2 X+2  X X^2+2 X^2+X X^2+2  0 X^2+X+2 X+2 X^2 X^2+X X^2  0  X  X  X  2  2 X+2 X+2  2 X^2 X^2+X X^2+X+2 X^2+2 X^2 X^2+X X^2+X X^2  0 X+2  X X^2  0  0 X^2+X+2 X^2+X+2 X^2+2 X^2+2 X^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+243x^56+128x^57+320x^58+128x^59+172x^60+16x^62+15x^64+1x^104

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 0.484 seconds.