The generator matrix

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

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+660x^56+672x^57+800x^58+524x^59+411x^60+308x^61+316x^62+116x^63+127x^64+44x^65+108x^66+7x^68+2x^72

The gray image is a code over GF(2) with n=472, k=12 and d=224.
This code was found by Heurico 1.16 in 23.7 seconds.