The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+78x^56+88x^57+78x^58+8x^61+1x^64+2x^66

The gray image is a code over GF(2) with n=456, k=8 and d=224.
This code was found by Heurico 1.16 in 0.062 seconds.