The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+311x^56+400x^57+312x^58+120x^59+261x^60+352x^61+200x^62+24x^63+46x^64+8x^66+6x^68+4x^72+3x^76

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 0.266 seconds.