The generator matrix

 1  0  1  1  1 X^2+X+2  1  1 X^2+2  1  1  2  1  1  X  1  1 X^2+X  1 X+2  1 X^2+X+2  1  1 X^2  1  1  1  1  2  1  1  X  1  1 X^2  1  1  2  1  1  X  X  1  1  1  X  1 X^2+X  X X^2+2 X^2+2  1  X X^2+X  1  1  1  2
 0  1 X+1 X^2+X+2 X^2+1  1  2 X^2+X+1  1 X^2+2 X+1  1  X  3  1 X^2 X^2+3  1  1  1 X^2+X  1 X^2+1 X^2+2  1 X+2 X^2+X+3 X^2+X X+1  1  0  3  1 X+2 X^2+X+3  1 X^2+X X+3  1 X+2  1  1  0 X^2+3  2  0 X+2 X^2+1  1  1  X  X X^2+3 X^2+X+2  1 X^2+2 X^2+X+1  2  1
 0  0 X^2 X^2  2 X^2 X^2+2 X^2+2  2  2  0 X^2+2 X^2+2  0 X^2+2 X^2 X^2  2 X^2+2  0  0 X^2+2  0  0 X^2  2  2  2  2 X^2  2  2 X^2  0  0 X^2+2 X^2+2 X^2+2  2 X^2 X^2  2  2 X^2+2 X^2 X^2+2  2 X^2  0  2  0 X^2  2 X^2+2 X^2+2  0  0  0 X^2
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  2  0  0  2  2  0  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  0  2  2  2  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  2  0  2

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+360x^56+256x^57+512x^58+48x^59+304x^60+176x^61+256x^62+16x^63+97x^64+16x^65+4x^72+2x^80

The gray image is a code over GF(2) with n=472, k=11 and d=224.
This code was found by Heurico 1.16 in 43.7 seconds.