The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+204x^56+128x^57+160x^58+16x^60+1x^64+2x^80

The gray image is a code over GF(2) with n=456, k=9 and d=224.
This code was found by Heurico 1.16 in 0.078 seconds.