The generator matrix

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

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+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 43.4 seconds.