The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2+X+2 X^2  1  1  1  1 X^2+X+2  1  1 X^2+2  1  1  1  X  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1 X+2  2  2  X  2  0 X^2 X^2+X+2  1 X^2  0  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3 X+2 X+1  1  2 X^2+X+3  1  1 X^2+X X+2  1  1 X^2 X+1  1 X^2+X  2 X^2+3 X^2+X+3 X^2+X+2 X+1 X^2+1 X^2+X+3  2 X^2+3 X^2+2 X^2+X X^2+X+2 X^2+X+2 X^2+X X+2 X^2+X+1  1  1  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X+1
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2+2 X^2 X^2+X+2 X^2+2 X^2+X+2 X^2  X X^2+2 X^2+X X^2+X X^2 X^2+X X^2+2 X^2+X+2 X^2+X X^2 X^2+X+2  X X+2  X  2  0 X^2+2  X X^2+X X^2+2 X^2+X X+2  0  2 X+2  0 X^2 X^2+X  2  0 X+2 X^2+2 X^2 X^2+X X^2  0  2  X X^2+2 X^2+X+2 X^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+275x^56+396x^57+373x^58+166x^59+251x^60+290x^61+173x^62+34x^63+60x^64+6x^65+8x^66+4x^68+4x^69+4x^70+1x^74+1x^76+1x^78

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 0.156 seconds.