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

generates a code of length 56 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+32x^53+56x^54+64x^55+718x^56+64x^57+56x^58+32x^59+1x^112

The gray image is a code over GF(2) with n=448, k=10 and d=212.
This code was found by Heurico 1.16 in 0.203 seconds.