The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+136x^55+22x^56+206x^57+30x^58+96x^59+8x^60+8x^63+1x^64+2x^66+2x^73

The gray image is a code over GF(2) with n=456, k=9 and d=220.
This code was found by Heurico 1.16 in 0.797 seconds.