The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+738x^56+520x^57+880x^58+480x^59+519x^60+176x^61+328x^62+160x^63+195x^64+8x^65+80x^66+9x^68+2x^76

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 127 seconds.