The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+76x^53+42x^54+16x^55+42x^56+64x^57+4x^58+4x^60+4x^61+2x^62+1x^64

The gray image is a code over GF(2) with n=440, k=8 and d=212.
This code was found by Heurico 1.16 in 0.328 seconds.