The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  X  X  1  1  X  X  1  1  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  1  1  1 2X+2
 0  2  0  2  0  2  0  2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2  0  2  2  2  0  2  2  2  0  0 2X 2X 2X+2 2X+2  0 2X 2X+2 2X+2 2X+2 2X+2  0  0 2X  2 2X  2 2X 2X+2 2X 2X+2  0 2X  0  2  0  2  0 2X  2 2X+2 2X
 0  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0 2X  0  0  0  0  0  0  0 2X 2X 2X  0 2X  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X 2X  0 2X  0  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+76x^56+128x^57+32x^58+16x^60+2x^72+1x^80

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 0.156 seconds.